Generation of Alfvenic (magnetohydrodynamic) vortices by the interaction of compressible plasma flows with magnetic-field-aligned blunt obstacles is modeled in terms of magnetohydrodynamics. It is found that periodic shedding of vortices with opposite vorticity is a robust feature of the interaction in a broad range of plasma parameters: for plasma beta from 0.025 to 0.5, and for the flow speeds from 0.1 to 0.99 of the fast magnetoacoustic speed. The Strouhal number is the dimensionless ratio of the blunt body diameter to the product of the period of vortex shedding and the inflow speed. It is found to be consistently in the range 0.15-0.25 in the whole range of parameters. The induced Alfvenic vortices are compressible and contain spiral-armed perturbations of the magnetic field strength and plasma mass density up to 50%-60% of the background values. The generated electric current also has the spiral-armed structuring.