Stress analysis of a Y-shaped plate with round corners is carried out as a thin plate bending problem and a plane elastic problem. Complex variable method and a rational mapping function of a sum of fractional expressions are used. An exact solution for the shape represented by the rational mapping function can be obtained. Stress distribution and stress concentration at the round corners are investigated. It is shown that stress concentration factors for Y-shaped plates are expressed with good accuracy by using a general formula for stress concentration factor. Loading condtions of bending out of plane, twisting, tension and bending in plane at the tip of strips are considered.