Center of rotation point source acts as a basic model of a seismic source with torque. Unlike seismological double pair source or just a pair of forces with torque, placed in an infinite homogeneous lossless and linear elastic medium, the center of rotation generates a pure shear wave, which is polarized as SH wave with respect to a plane of incidence containing the torque vector. The presence of a free plane surface orthogonal to the torque direction causes a trivial SH reflection. The wavefield changes fundamentally with an increase in the slope of the source. We present our research on a problem with an arbitrarily oriented center of rotation placed in an elastic half-space.