The accurate modeling of continuum-rarefied gas flows is crucial for understanding non-equilibrium phenomena in aerospace applications, particularly for high-speed vehicles encountering rarefied flow conditions. Traditional Navier–Stokes-Fourier equations fail to capture these effects, while kinetic approaches like the Boltzmann equation are computationally prohibitive. The regularized 13-moment (R13) equations offer a promising alternative by bridging the gap between continuum and rarefied regimes with improved accuracy and computational efficiency. This study investigates the application of the R13 equations to simulate gas flow over aerospike blunt bodies, a geometry known for its aerodynamic and thermal efficiency in high-speed conditions. The R13 framework effectively captures non-equilibrium phenomena, which are critical in transitional flow regimes. For numerical simulations, a two-dimensional modal discontinuous Galerkin method is developed to solve the R13 equations. Key flow characteristics, such as shock wave interactions, rarefaction effects, and aerodynamics coefficients, are analysed to assess the performance of the R13 model. The findings demonstrate the capability of the R13 equations to accurately predict flow behavior across a wide range of Knudsen numbers while maintaining computational efficiency.