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A fast method, working in the frequency domain, has been developed for the simulation of the wave propagation on coupled microstrip lines. Precondition is the validity of the transmission line theory, that means a transversal electromagnetic wave-propagation on the transmission line systems is assumed. Then, the dynamic behaviour of lossless transmission line systems can be described by inductance- and capacitance-matrices which are submatrices of the system matrix of the problem describing vector differential equation. Its solution is given by the calculation of the transition matrix which is obtained by computing the matrix exponential of the system matrix. As this matrix is very easy structured and the above described submatrices are symmetric, the direct calculation of the transition matrix is necessary only for one basic frequency /spl omega//sub 0/ in order to solve the problem. The transition matrices for integer multiples of /spl omega//sub 0/ can be computed by easy and very fast matrix calculations.