In this article we reviewed the shock wave oscillation that occurs when supersonic flows interact with conic, blunt or flat nose of aircraft, taking into account the aerospike attached to it. The main attention was paid to the problem of numerical modeling of such oscillation, flow regime classification, and cases where aerospike attachment can lead to drag reduction. It is established that the effective computation methods, that allow acquisition and recreation of their oscillation, are based on either technique with pre-allocation on gas-dynamic discontinuities or high accuracy difference schemes. Moreover, the application of standard straight-through methods leads to appearance of non-physical artifacts in solution: solution's oscillation on shock waves, weak rarefaction waves and instability streets of Kelvin-Helmholtz type. The practical value is that the research findings may be useful for future investigations on the problem of numerical modeling of shock wave oscillation.