The article is devoted to deriving reference models for the problem of initial alignment of a strapdown inertial navigation system (INS) on a swing base. It is assumed that the system does not move relative to the Earth, but its body can make uncontrolled angular motions. The described models are based on the approximation of the readings of INS accelerometers from projections on the axes of the instrument reference frame “frozen” in the inertial space, and the orientation of the frame is determined by its position at the start of the alignment.