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The arcticle gives a spatial gas-dynamic formulation of the backpressure problem, which describes the change in pressure in front of an accelerating projectile when it moves along the bore. This takes into account the geometry of the front of the projectile and its influence on the formation of the shock wave. An unsteady spatial flow of the displaced medium ahead of the projectile body without and taking into account the forces of viscosity is considered. The paper considers the solution to the problem of throwing a body using the energy of gunpowder combustion. The internal ballistics problem, which determines the dynamics of the projectile movement, is solved in terms of averaged parameters. A two-step Runge-Kutta scheme with a second order of accuracy is used to numerically integrate a system of ordinary differential equations in time. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the problem of the decay of an arbitrary discontinuity. A comparison is presented of taking into account the backpressure as the pressure behind the detached shock wave, obtained from the analytical solution of the problem of the supersonic motion of a flat piston in a pipe at a constant velocity, and the pressure acting on the projectile, determined from the solution of nonstationary one-dimensional and spatial (axisymmetric) equations of gas dynamics. It was found that taking into account the viscosity practically does not affect the results of calculating the backpressure, while taking into account the shape of the front part of the projectile leads to a significant difference in the pressure fields behind the front of the shock wave compared to the solution in the framework of the one-dimensional formulation of the problem, where the shape of the front part of the projectile cannot be taken into account. It is concluded that this can significantly affect the results of modeling the ballistics of a shot at high throwing speeds.