Numerical calculations in a framework of 2-D axisymmetric unsteady Euler equations are performed and compared with some known experiments with laser-induced energy deposition located in supersonic flow upstream of different bodies. The single energy impulse interaction with a sphere in the air flow at M∞ = 3.45 is investigated. The complex unsteady flowfield structure is analyzed and compared with experimental data as well as with known calculations on the basis of the Navier-Stokes equations with the real gas effects modeling. Experimental evolution of surface pressure distributions on the sphere is compared with calculated one in a framework of ideal and viscous gas models. The results of parametrical numerical research of the flowfield features in a vicinity of blunt spherical and sharp conical axisymmetrical bodies in conditions of the periodic pulse energy deposition in flow of argon is performed at M∞ = 2. Comparison with experiments on the flowfield and wave drag variation for the range of energy source frequency f = 12.5 - 100 kHz is carried our. Similar calculations for the cases with the equivalent steady energy deposition are analyzed also. Additional possibilities of the wave drag reduction by a variation of energy source length as well as its frequency are demonstrated.