Detailed discussions are given to the problem of minimizing the theoretical wave resistance with special reference to the existence of the solution of the calculus of variation. Rigorous solutions are given to the integral equations which express the condition of the minimum wave resistance of strut-like ship forms with infinite draft under various side conditions. The solution determines the optimnm shape of water line. Optimum curves of sectional area of slender ships are calculated in a similar way. Resistance experiments are carried out with respect to the optimum forms, showing a good agreement with the theoretical result.