Considering epicyclic oscillations of pressure-supported perfect fluid tori orbiting Kerr black holes we examine non-geodesic (pressure) effects on the epicyclic modes properties. Using a perturbation method we derive fully general relativistic formulasfor eigenfunctions and eigenfrequencies of the radial and vertical epicyclic modes of a slightly non-slender, constant specific angular momentum torus up to second-order accuracy with respect to the torus thickness.