The plate under shear loading umformly distributed on the end portions of its side boundary was considered. Infinite hyperbolic serieses and Fourier serieses were combined as a stress function and from which exact solutions for the 15 cases for the parameters of b/L=0.25, 0.5, 1.0 and l/L=0.2, 0.4, 0.6, 0.8, 1.0 are obtained. In each cases the first 5 terms of the infinite series at the 36 points as shown in Fig. 3. The results are presented in Fig. 4-1, 4-2, and 4-3. The conclusions are as follows: 1) The stresses ${sigma}_x$ increase very slightly as $chi$ increases in the range of 0<x<L-l 2) When the parameters satisfy the conditions b/L<0.25 and l/L<0.2, the stresses in the region of 0<x<L-l can be obtained by replacing the uniform shear loading by the equivalent uniform shear loading by the equivalent uniform tensile force and pure bending moment at x=l. 3) The stress ${sigma}_y$ is negligible throughout the region. 4) When the parameter b/L varies, the stresses ${sigma}_x$ and u vary as L/b, while strain $upsilon$ varies as $(L/b)^2$.