A non-linear, two-dimensional, resistive MHD computer code to study the non-linear behaviour of the m = 0, 1, and 2 tearing modes in a reversed field pinch is used. For the cases m ≠ 0, a co-ordinate transformation which assumes helical symmetry is employed to reduce the dimensionality of the problem from three to two. The force-free Bessel function model equilibrium is used. It is found that the most dangerous resistive instability in this case is the m = 1 tearing mode, because of its larger growth rate and extended period of exponential growth.