Based on the coupled combustion model of mixed solid fuel, unsteady combustion of fuel was studied when the pressure was changed in the combustion chamber of a model controlled small solid fuel engine. Modeling of engine thrust control system was carried out in two ways: by changing the critical section area of the nozzle over time according to a given law and by changing the area of the burning surface of the fuel according to a given law. It is found that with a sharp increase in pressure, the combustion rate increases above the quasi-stationary value, which leads to an increase in the pressure in the combustion chamber above that calculated from the quasi-stationary rate. With a sharp decrease in pressure, the combustion rate decreases to a value less than the quasi-stationary rate at the corresponding pressure. The decrease in the combustion rate leads to a decrease in the pressure in the combustion chamber below that calculated from the quasi-stationary rate. At small values of the characteristic relaxation time of the combustion chamber, a sharp decrease in pressure in the combustion chamber will lead to the extinction of the charge combustion.