Abstract: During the experiment on mechanics of materials, a problem of solid circular shaft in torsion testing for large deformation remains unsolved. The following formula for torsional shearing stress at a point on the suface of a shaft is derived by the author. That is τ=1/(2πR³)(3M_n+φ(dM_n)/(dφ))-(M_nφ²)/(πR(l²+R²φ²)) The applied torque and corresponding angle of twist are measured by a torsion-testing machine, and the data are eventually calculated by a computer. So, the complete shearing strew-shearing strain diagram may be drawn.