In this paper, the boundary layer around a rotating circular cylinder in an axial uniform flow is discussed both theoretically and experimentally. The problem has not been exactly dealt with because of its difficulty, although it is one of the most fundamental and important problems in the field of the three dimensional boundary layer theory. Theoretical investigations are made with the use of the finite element method solving the Navier-Stokes equations and experiments are carried out in the circulating water tunnel. The Laser Doppler Velocimeter is used to measure the velocities in the boundary layer. The results obtained by numerical and experimental investigations are qualitatively in good accordance with each other. Conclusions obtained in this paper are summarized as follows ; 1° The boundary layer around a rotating circular cylinder is analogous to that of a yawed flat plate in relatively wide range of the rotation parameter ; 2° The rotation causes the point of inflexion in the axial velocity profile, which may make the flow turbulent ; 3° The boundary layer around a slowly oscillating circular cylinder is analyzed approximately, which is effective for the estimation of the viscous damping force of the lateral oscillation of a ship in advance.