Shared-memory vector multiprocessors like the IBM 3090 complex offer to scientists and engineers the possibility of reducing considerably the elapsed time to solve large problems by using more than one CPU within a single application. The exploitation of parallelism complements the benefits of vectorization obtained by (pipelined) vector units and overcomes the limitations of hardware technology. Most of the existing scientific and engineering applications have been designed, however, for serial (uniprocessor) execution. These applications have now to be restructed and possibly redesigned for efficient exploitation of parallel computer architectures. For the parallelization of existing and new applications IBM offers Parallel FORTRAN which is a superset of the well-known VS FORTRAN vectorizing compiler. This paper presents an introduction to the parallelization of engineering problems with the aid of an example. The paper includes a description of the new Parallel FORTRAN language extensions and its implementation under the MVS and VM operating systems on the IBM 3090 multiprocessor, an analysis of parallelization strategies for the problems and a discussion of the performance resulting from the parallelization. It is shown that problems with sufficiently large amount of arithmetic operations within the parallel tasks are efficiently parallelized, obtaining speedups of more than three on the IBM 3090 four-processor system with small programming effort. This paper can be seen as the first hands-on experience of the authors with the implementation of engineering applications with the IBM Parallel FORTRAN.