The electric and magnetic circuits of electrical machines are generally so complex that the exact evaluation of such quantities as leakage reactance and a.c. resistance is virtually impossible. With the advent of digital computers it has become feasible to develop numerical methods of predetermining the flux pattern in such cases. In the paper the finite-difference equations for electromagnetic systems are obtained, and the inductance is calculated by integrating the magnetic vector potential over conducting surfaces. The same finite-difference equations are applied to the calculation of a.c. resistance of conductors in slots. The use of the method is illustrated by examples of standard transformers, a tap-changing transformer, calculation of the leakage reactance of the field winding of a salient-pole-alternator and the screening of d.c. poles in a new type of oscillating synchronous linear machine.