Abstract We investigate the dispersive properties of a nonconforming finite element method (NC-method) to solve the three-dimensional scalar and elastic wave equations. The study is performed by constructing and analyzing the dispersion relations, and by evaluating derived quantities such as dimensionless phase and group velocities. The behaviour of the present algorithm is compared with that of a conforming finite element method (C-method) with the same order of spatial approximation. It is observed that the NC-method introduces less numerical anisotropy and dispersion than the C-method, allowing to work with fewer than 10 points per wavelength with reasonably small relative errors. On the other hand, the computational cost of the NC-method is higher than that of the C-method. However, the present NC-method is suitable for domain decomposed parallel algorithms; therefore the fact that the NC-method needs more computing time may be partially compensated by its lower transmission load.