We present a snapshot imaging Mueller matrix polarimeter using modified Savart polariscopes (MSP-SIMMP). The MSP-SIMMP contains both the polarizing optics and the analyzing optics encoding all Mueller matrix components of the sample into the interferogram by the spatial modulation technique. An interference model and the methods of reconstruction and calibration are discussed. To demonstrate the feasibility of the proposed MSP-SIMMP, the numerical simulation and the laboratory experiment of a design example are presented. The remarkable advantage of the MSP-SIMMP is easy to calibrate. Moreover, compared with conventional imaging Mueller matrix polarimeters with rotating parts, the advantage of the proposed instrument is simple, compact, snapshot-enabled, and stationary (no moving parts). (c) 2023 Optica Publishing Group