The response of the offshore drilling platform to seismic base excitation is analyzed. The platform is a spatial construction made of metal rolled pipes of various diameters. The connection of pipes is done by welding and on bolts. All joints of the construction model are considered to be rigid when analyzed. A modal analysis of the construction was performed and modal effective masses as well as modal participation factors corresponding to eigenmodes were defined. The analysis of the modal participation factors showed that the greatest contribution to the seismic response was given by the first four mode shapes with almost thirty percent of the total modal mass contributed by the second mode shape. This mode shape turned out to be similar to the mode of deformation of the console rod that bends in the plane of greatest stiffness. The synthesized artificial spectrum-compatible seismic accelerograms were selected from the set included in the state building codes using oscillation period corresponding to the second natural frequency. The response of the platform to the earthquake of seismic intensity 9th degree according to the Medvedev-Sponheuer-Karnik scale was investigated. Two methods of the seismic analysis were used. The first one was the linear quasi static Response Spectrum Method and the second one was Direct Dynamic (Time History Analysis) Method. The results of calculations carried out using the Direct Dynamic Method were averaged on the whole time interval and the data of such an averaging were compared with the results of the Response Spectrum Method application. The results proved to be consistent with each other - the difference does not exceed one percent for displacements and five percent for internal forces and moments. This circumstance indicates the reliability of the results obtained with the help of two different methods.