We study epicyclic oscillations of thick relativistic tori with constant specific angular momentum distribution using the finite element numerical method. We have compared frequencies of the axisymmetric and non-axisymmetric modes with the analytic formulae obtained by Straub and Šrámková (2009) and Fragile et al. (2016). We have found excellent agreement in the case of axisymmetric radial epicyclic modes. In the case of the axisymmetric vertical epicyclic modes and non-axisymmetric modes in general, the analytic approximation agrees with numerical results only for tori of moderate thicknesses. Our analysis also revealed an instability of the thick constant angular momentum tori with respect to the radial epicyclic oscillations.