We present the software package hybridMT which allows performing seismic moment tensor inversion and refinement, optimized for earthquake data recorded by regional‐to‐local seismic networks as well as for acoustic emission activity. The provided software package is designed predominantly for use in MATLAB (see Data and Resources)/shell environments. The algorithm uses first P‐wave amplitudes to invert for unconstrained full, deviatoric, and double‐couple constrained moment tensors. Uncertainty assessment is performed by bootstrap resampling. The moment tensor inversion may be performed directly in the shell environment (by a dedicated command‐line tool) or conveniently through the MATLAB interface (m‐functions). In addition to moment tensor inversion, we also provide the MATLAB implementation of the hybrid moment tensor technique. This methodology increases the quality of calculated seismic moment tensors from events forming a spatial cluster by assessing and correcting for poorly known path and site effects. We tested hybridMT on synthetic datasets, acoustic emission data recorded during laboratory rock deformation experiments, and induced seismicity data from a geothermal reservoir. The package is supplemented with extensive documentation, tutorials, and a dedicated website. HybridMT is freely available and distributed under General Public License.