The code TOKSCEN (TOKamak SCENario) for the modelling of plasma evolution is described in this paper. The modelling is based on numerical solution of the Grad–Shafranov equation of plasma equilibrium and circuit equations for eddy currents at each time step. The circuit equations for eddy currents are solved in matrix form using the technique of matrix inversion. The plasma current distribution should be given. The code enables the calculation of an increment of vertical instability at each time step of the plasma evolution. The algorithms of the code were used for the modelling of processes in KTM and other tokamaks.