The advent of parallel computers will have an important impact on many areas of science. The speeds available are up to ten or even twenty times that of computers currently available to university scientists, however this speed is only achieved if algorithms and programming techniques are tailored to the architecture of the computer. The architectures of two of the most advanced parallel computers, the CRAY-1 and the ICL DAP are described and contrasted. This is followed by the description of three examples where important new scientific or engineering results are being obtained by computer simulation. These are in the study of galactic evolution, the design of sub-micrometre semiconducting devices and the study of the amorphous state. All these applications presently consume many hours of IBM 360/195 time per case and the extra speed of the parallel computer is required if the full benefit of such simulation studies is to be realised. Many other examples of the contributions that such computers can make to British science are given and the case is made for the acquisition of a CRAY-1 computer in the University sector. The case is also made for treating Computational Science as an independent academic discipline in order that future scientists have an adequate background to exploit these new computational resources.