Intravascular ultrasound (IVUS) is a medical imaging modality aimed at imaging blood vessel walls from within the vessel. Current commercial IVUS catheters are designed to yield two-dimensional cross-sectional images perpendicular to the vessel wall. By pulling the catheter back through the artery (in the ‘axial direction’), and stacking the resulting cross-sectional images, a three-dimensional image of the artery can be obtained. However, in non-stationary blood vessels like, e.g., the coronary arteries, artery motion is added to the pullback motion, and as a result consecutively obtained cross-sectional images are not necessarily acquired in neighbouring positions. Therefore, IVUS measurements are electrogated to ensure proper localisation of the consecutive cross-sectional images. Unfortunately, the radiation pattern of commercial catheters is very narrow, which, combined with a high pullback rate, leads to severe spatial undersampling in the axial direction. Consequently, the data is incomplete and motion compensation attempts are unsuccessful. Instead, in this work the design of an axial IVUS array is presented. With the array, three-dimensional volumes rather than cross-sectional planes are imaged in each pullback position. If the imaged volume is large enough, overlap between images from consecutive electrogated measurements can be achieved. This enables motion compensation techniques, as well as the acquisition of continuous, correct three-dimensional images of artery sections. In order to assess the image quality of the resulting prototype design, software has been developed which models linear acoustic propagation through inhomogeneous soft tissue. The resulting scattering is not limited to the Born approximation. The governing frequency domain integral equation is solved iteratively using a parallelised Fortran implementation, which is accurate to within several percent when compared to analytical solutions. Arbitrary contrasts in both compressibility and volume density of mass, as well as arbitrary transducer configurations can be treated. Unfortunately, where contrasts extend the numerical domain boundaries, spurious reflections are generated. These reflections are suppressed by a factor of one hundred or more using a frequency domain scatter integral equation formulation of a perfectly matched layer, while virtually no reflections occur off this attenuative layer. Both the scatter simulation software and the design of an ultrasound array require the accurate and efficient computation of incident pressure fields generated by a (piston) transducer. Five methods are compared in efficiency and accuracy, viz. the Rayleigh integral, the impulse response method, the fast near-field method, the fast near-field method combined with time-space decomposition, and a frequency domain formulation of the latter time-space decomposition method. The frequency domain formulation has been derived to extend the validity of the time-space decomposition method. To reach the same accuracy, the fast near-field method and time-space decomposition easily yield a speed-up factor of more than one hundred when compared to the Rayleigh integral, and the maximum attainable accuracy is significantly higher for these methods. Note that, apart from the Rayleigh integral, all methods assume piston behaviour of the transducer. The fast near-field method was used to design an optimal axial IVUS array given the constraints in dimensions, frequency, penetration depth and sensitivity. The resulting array consists of eight elements of dimensions 100 µm by 350 µm, with an interelement kerf of 100 µm, and operates at 20 MHz. Using the scatter simulation software, the expected image quality is simulated, and significant improvements over the image quality of a current commercial catheter are achieved. The array prototype was fabricated in-house by first fabricating piezo-electric wafers including matching and backing layers. Next, the electrical connections were made, and finally the separate elements were diced from the wafer. The resulting array contains almost identical elements operating at 21 MHz, with a fractional bandwidth of 80 % or more. Using far-field pressure field measurements, the transducer surface velocity distribution was computed using an iterative inversion scheme. From this measurement it followed that, despite the complicated construction, the elements vibrate independently, and that motion is spatially confined to the actively driven regions. Using both reference phantoms and a bovine artery, the image quality of the array prototype was compared to that of a conventional single element IVUS catheter. In the radial and axial direction the array yields a significantly higher image quality, while in the circumferential direction a similar image quality was obtained. With the array prototype, contrast boundaries are smoothly and continuously imaged in the axial direction, and local events are properly localised. In addition, using the array prototype both the wires of a stent phantom and the structure behind the wires can be imaged, whereas using a conventional single element transducer only the wires are visible, and smeared out in the axial direction.