The use of the finite elements (FES) method for the computation of unsteady gas flow through the intake and exhaust pipes of a multi-cylinder engine set forth by the authors at the Congress of CIMAC’87 has been further developed by adapting a model with hybrid FEs; the model is based on the continuity-discontinuity duality. The state parameters of gases in a finite element (FE) have been broken into 1) field variables and 2) variables independent of spatial coordinates; the former allow continuity conditions in the knots whereas the latter do not; 3) compound variables. Gas state along the intake and exhaust lay-out has been defined as a system of four differential equations with partial derivatives of hyperbolic type which consider the fluid as compressible, viscous, in unsteady flow, with varying composition throughout its lay-outs. The strategy for solving the system consists in the change from partial derivative equations with respect to time and space to ordinary differential equations with respect to time only. The method has been applied to a 4-cylinder diesel car engine and computing results are compared to experimental data.