This paper summarizes the formulation, implementation and preliminary application of a coupled fluid-structure-combustion algorithm developed to simulate convective burning in stationary and dynamically propagating cracks present in solid propellant specimen. The coupling approach combines an explicit cohesive/volumetric finite element (CVFE) scheme, used to model the spontaneous initiation and rapid propagation of cracks, with an unstructured adaptive finite volume fluid solver. A dynamic burning module models the transient combustion process in the solid-propellant crack cavity. An Arbitrary Lagrangian /Eulerian (ALE) formulation is adopted for the solid solver to account for the regressing boundary of the solid propellant. The code is applied to two problems: one involves convective burning inside a stationary crack, regression of the solid walls and flame spreading along the crack. The second problem involves the simulation of crack propagation due to the convective burning and the corresponding pressurization in solid propellants.