In blasting excavation, the operation is always close to existing tunnels. It is not suitable to treat blasting waves as plane waves. In this paper, blasting waves are simplified as cylindrical P-waves. The wave function expansion method and multi-polar coordinates are adopted to derive the formula for dynamic stress concentration factor (DSCF) of tunnel surrounding rock under cylindrical P-waves. Combined with a specific engineering case, the influence of frequency and scaled distance r* on DSCF is analyzed. Results show when when r* is small, the increasing frequency of the incident wave will result in a more complex distribution of DSCF and the change in the location of the maximum DSCF around the metro tunnel from θ = 0° to θ = 180°, but the maximum DSCF around the metro tunnel increases first and then decreases, and the highest value is at about 20 Hz; the distribution of DSCF induced by cylindrical P-waves is quite different from plane incident P-waves. With the increase of r*, the maximum DSCF around the metro tunnel tends to be a constant of about 2.39 and the distribution of DSCF changes towards to the case of plane P-waves; when r* ≥ 15, a cylindrical P-wave can be approximately treated as a plane P-wave.