This paper deals with stress concentration problems of a hollow circular thick walled elastic cylinder with a semicircular groove under internal pressures. A method of solution is presented for the problem by applying Green's functions for axisymmetric body force problems of a thick elastic plate. The Green's functions are defined as solutions for a thick elastic plate subjected to axisymmetric body forces acting along a circle in the interior of the plate. Stress concentrations at the groove are investigated by numerical calculations.