In this paper, internal ballistics of solid rocket motors (SRM), in which the grain is burned from inside (inner burning surface) or from both inside and outside (inner and outer burning surfaces), is numerically simulated. The solution domain includes two passages and a converging-diverging nozzle. It is discretized using a control-volume finite-element method. Governing equations of the quasi one-dimensional Euler flow are integrated over each control volume. The flux-vector components are related to the nodal values using a physical influence scheme. Erosive burning is incorporated in the flowfield calculation using a quasi-steady model. In cases with inner and outer burning surfaces, the resulting system of equations deviates from a block tri-diagonal one. Therefore, special care is needed for the efficient solution of this system of equations. To evaluate performance of the present algorithm, transient flow fields of several SRMs with different burning surfaces are simulated, and the results compared with the experimental data and numerical results. The excellent agreement observed in all cases validates the algorithm and approves its accuracy. For SRMs with inner and outer burning surfaces, possibility of their modeling with an equivalent motor is also investigated. In addition, a SRM with area transition along the grain is simulated to demonstrate the general capability of the present code.