Rotary-vane engine (RVE) with an external supply of heat is an aggregate consisting of two modules with a common output shaft, the heating device (heater) of working medium and the cooling device (cooler) of working medium, which connected with inlet and outlet ports of modules by system of pipeworks. Each module has two rotors with two vanes on each. Between the corresponding plane surfaces of the four vanes four working volumes are formed wherein thermodynamic cycle steps: ingress, compressing, heat intake, expansion stroke, discharge, outward heat transmission are going simultaneously. The angular displacement of modules relative to one another occurs pumping the working medium through the heater and cooler, which allows the conversion of thermal energy into mechanical work. Design features of the RVE with an external supply of heat allows create a closed gas-vapor cycle. The main specified advantages of the RVE with an external supply of heat are: fewer noxious emissions, multifuel capability, high motor potential (service life). Different problems of creation external combustion engines such as structural complexity of construction units, absence of adequate mathematical model of designed RVE with an external supply of heat are also pointed. The construction of the RVE with an external supply of heat developed in Pskov Polytechnic Institute (now the Pskov State University), the operation concept of the engine, the physical processes in the chamber modules RVE with an external supply of heat during each step and the mathematical model describing the physical processes proceeding in chamber RVE with an external supply of heat modules are considered.