The paper refers to the dynamic short-term response analysis of the Baltic steel drilling platform (see Fig.2) in a random sea-state represented by one-dimensional wave spectrum proposed by Striekalov and Massel, which is recommended for the Baltic Sea area. The Baltic drilling platform is a jack-up type platform for the exploration and exploitation of oil under the Baltic Sea. The presented analysis deals with the stationary phase of the platform life when its legs are fixed in the sea bottom. The submerged elements of jack-up platforms are relatively slender, thus to assess the in-line wave forces a modified Morison equation is justified. The application of frequency transfer functions to offshore vibration systems leads to structural response spectra whose input is defined by the wave elevation and wind velocity spectra. The analysis can be applied also to support structures for offshore wind turbines.