In order to find the means of improving the hull efficiency of the single screw ship, a methodis proposed to culculate theoretically the thrust deduction coefficient. Principal assumptionsbeing; (i) the hull is the cylinder with vertical generating lines, (ii) the induced velocity causedby the propeller is obtained by the doublets uniformly distributed over the propeller disk. If the water plane shape is represented by the third power series of the distance from the propeller, the thrust deduction coefficient is to be computed by the following formula. t=1/π(√s+1>+1){2(2α/1-w+√s1>-1)(y₁/R-I₁)-(√s+1>-1)I₂} where, c_s : the thrust loading coefficient, α: the effective velocity factor along the surface of run, y₁ : a half maximum breadth of the hull, R : the radius of the propeller, I₁ , I₂ : the functionof the hull shape only. Provided that c_s is not too large, the above formula can be approximated by t=4α/π(√s+1>+1)(1-w)(y₁/R-I₁) The principal conclusions are following:- 1. t grows smaller as w, c_s , ε₀ (the angle of run) or the propeller immersion grows smaller. 2. t grows smaller as the Reynolds' number or the clearance between the propeller and the stern frame grows larger. 3. The hull efficiency grows larger as the Reynolds' number or t due to the hull shape grows smaller. 4. The most practical and effective means to improve the hull efficiency is to reduce the angle of run or to widen the clearance between the propeller and the stern frame.