The preparation of specimens from a rigid polyurethane containing montmorillonite (MMT) particles as a filler is described. The specimens were fabricated employing a biopolyol synthesized from rapeseed oil. The investigation of their structure was performed by using the X-ray diffraction analysis. The thermomechanical properties of the specimens were determined by means of a dynamic mechanical analysis at temperatures varying from 20 to 160°C. Experimental data on the influence of MMT additions on the mechanical properties (hardness, strength, elastic modulus, ultimate elongation, and creep) of the composite are obtained. A theoretical analysis of elastic properties of the composite is carried out by using the Mori–Tanaka theory of an equivalent medium. The calculation results are compared with experimental data.