A frame for use in a construction machine such as a hydraulic excavator, in which a circle member (18) for mounting a swing circle to a center frame is secured. An outer curved portion (21A) with a recessed groove shape is provided over the entire circumference in a vertically intermediate portion of the outer peripheral surface of the circle member, and an inner curved portion (21B) with a recessed groove shape is provided over the entire circumference in a vertically intermediate portion of the inner peripheral surface of the circle member to thereby make it possible to render small the plate thickness (t) of the hourglass-shaped thin-walled portion (21) located in the vertically intermediate portion relative to the plate thickness (T) of upper and lower thick-walled portions (19, 20) located on both vertical end sides of the circle member. Consequently, the weight of the circle member can be reduced.