Abstract The Zoned Finite Strip method, where one strip can have several different materials in the horizontal direction, has been extended for dynamic problems. Eigenfrequencies and eigenmodes are calculated e.g. in order to perform a response spectra analysis in the case of an earthquake loading. Besides the new dynamic capabilities, some improvements are proposed for the static case. Also some very efficient solution methods, specially for finite strip problems, are included and commented upon. The extensions have been applied to three different problems and the results are compared with analytical and numerical (finite element) methods. The examples show good agreement between the different methods.