ParallelNuscaS is an object-oriented package for parallel finite elemt modeling, developed at the Technical University of Częstochowa. This paper is devoted to the investigation of the package performance on the ACCORD cluster, which this year was built in the Institute of Mathematics and Computer Science of this University. At present, ACCORD contains 18 Pentium III 750 MHz processors, or 9 SMP nodes, connected both by the fast MYRINET network and standard Fast Ethernet, as well as 8 SMP nodes with 16 AMD Athlon MP 1.2 GHZ processors. We discuss the implementation and performance of parallel FEM computations not only for the message-passing model of parallel programming, but also for the hybrid model, which is a mixture of multithreading inside SMP nodes and message passing between them.