Accurate knowledge of the seismic material properties in the immediate vicinity of the receivers represents a prerequisite for elastic wavefield decomposition. We present strategies for estimating the elastic material properties for both land and seabed multicomponent seismic data. The proposed scheme for land data requires dense multicomponent geophone configurations, which allow spatial wavefield derivatives to be explicitly calculated. The required information can be obtained with four three‐component surface geophones positioned at the corners of a square, and a fifth geophone buried at a shallow depth below the center of the square. The technique yields local estimates of the near‐surface P‐ and S‐wave velocities, but the density cannot be constrained. Using a similar approach for four‐component (three orthogonal components of particle velocity plus pressure) seabed recordings allows the P‐ and S‐wave velocities as well as the density of the seafloor to be estimated. In this case, the proposed scheme does not require buried geophones, and it is applicable to multicomponent data recorded in routine seabed surveys. Compared to existing techniques, the new method allows the elastic sea‐floor properties to be more accurately determined, and it does not rely critically on the inclusion of large‐offset data. Numerical tests indicate that the proposed schemes are robust and yield accurate results, provided that the signal used for the inversion contains sufficient horizontal energy and can be clearly identified and separated from other signals. Although the schemes are designed for application on the first arrivals, they are, in principle, applicable to any data window containing isolated P‐ or S‐arrivals. The proposed scheme is successfully applied to a seabed data set acquired in the North Sea. In contrast, the application on a multicomponent land data set was unsuccessful, because of strong receiver‐to‐receiver variations in amplitude and phase, probably caused by differences in coupling and instrument response.