Scientific programmers are eager to exploit the computational power offered by Distributed Memory Parallel Computers (DMPCs), but are generally reluctant to undertake the manual porting of their application programs onto such machines. A possible solution to this problem consists in using libraries that hide the details of parallel computations. We show how to go one step beyond, using the full power of modern object-oriented languages to build generic, extensible object-oriented libraries that permit an efficient and transparent use of DMPCs. In EPEE, our Eiffel Parallel Execution Environment, we propose to use a kind of parallelism known as data-parallelism, encapsulated within classes of the Eiffel sequential object-oriented language, using the SPMD (Single Program Multiple Data) programming model. We describe our method for designing with this environment a truly object-oriented linear algebra library for DMPCs. In the conclusion, we enumerate the advantages of our approach and make a few prospective remarks.