A model of solid propellant erosive burning is developed. Reciprocal interaction of turbulence with chemical reaction is taken into account by considering correlations for turbulent heat transfer affected by combustion reaction in the flame zone and developing an expression for the averaged value of combustion reaction rate. A local-isotropic assumption is invoked to reduce the full transport equations for turbulent fluctuations to simple formulas. Erosive burning of stick propellant is studied numerically by a boundary-layer approach. Satisfactory agreement with measurements is obtained using the proposed model both with the full transport equation and with the local-isotropic assumption. A new physical mechanism of negative erosive burning (decrease of propellant burning rate under blowing of burning surface) is proposed and confirmed by numerical investigations of stick propellant burning by using a mathematical model that is described by two-dimensional Navier-Stokes equations.