Abstract <p>A laminar steady flow around an axisymmetric body is investigated. The body rotates with a constant angular velocity in an incompressible viscous fluid obeying the Navier–Stokes equations. It is assumed that the body shape is generated by a periodic curve and only slightly deviates from a cylinder. A solution in the form of a truncated power series is obtained. The solution is in close agreement with the numerical results obtained using the pseudo-spectral method.</p>