To investigate the seal dynamic instability for a misaligned and coned mechanical face seal, the finite difference approximation was employed to solve the modified Reynolds equation for an incompressible fluid and temperature dependent viscosity. Using the solution, the results for axial force, transverse moment, restoring moment, and ratio of the transverse moment and the restoring moment are calculated for the whole range from zero to full angular misalignment. The results indicate that the transverse moment due to the angular misalignment and coning terms affects considerably the dynamic instability of face seals. It is shown that the simplified treatment of Reynolds equation using the narrow seal approximation overestimate the ratio of the transverse moment to the restoring moment especially at touch.