In the following paper, the author investigates mathematically the wave resistance of a sphere moving parallel to the free surface of a shallow sea. Correcting the errors committed by T. H. Havelock and others, he has obtained a new formula, and has carried out numerical calculations, the results of which are shown in several diagrams. The new formula is R=πA2c2 /ρ∫=π/2Φ0K3secΦ (1+tanh Kh)2/gsec2Φ (c2-ghsec2Φ) +K2c4h (e-f1K+e-fK) 2dΦ. where R=the wave resistance A= ρgα3 α=the radius of the sphere ρ=the density of the fluid g=the acceleration due to gravity c=the velocity of the sphere h=the depth of the fluid f1 = the immersion of the sphere f2=the immersion of the image of the sphere or =2h-f1K and Φ0, the lower limit of integration, are to satisfy the following relations respectively. Kc2 = g sec2Φtanh Kh (c2<gh sec2 Φ) Φ0=0 when c2<gh Φ0=cos-1 (gh/c2)1/2 when c2>gh Finally, the author makes some discussions on the results obtained, especially on the diagrams, and compares them with certain experimental ones.