Semi-discrete method is known since 80's of XX^th century. The method provides analytical solution in time, so the time-stepping may be omitted. Comparing to usual finite elements method in time, this method seems not to be numerically effective, because produced matrices are dense. Because of this reason, it was rather rarely used. However to carry out sensitivity analysis with adjoint models [1] solutions in forward and backward time have to be obtained. Both time points should coincide. For space discretization finite elements are used, as usual. The semi-discrete method allows to determine analytically the continuous solution for any given time of analysis. In this paper evaluation of this method for different kinds of excitation shapes is presented. The sensitivity analysis is applied for inverse task of recognition of conductivity distribution in non-destructive testing of materials using eddy-currents.