Abstract: The author derives in this paper a general formula which expresses the relation of rolling torque T to roll size R, contact angle θ, forward and backward tensions Sf and Sb, yield strength Ko, and external coefficient of friction μ as follows: T =R2K/2sinθsin (No + θ), where Nθ is determined by the state of stress at the paint φ= θ. This problem has been studied fruitfully in the experimental aspect. In this paper, however, the author has solved this problem theoretically. The correctness of this formula is shown by checking with some experimental results selected from Hessenberg and Sims’ experiments (1952).