It is known that the composite material shafts using on small boats have various advantages comparing to forged steel shafts, fur examples, specific strength, fatigue strength, corrosion, etc. The analysis of the stresses and strains in the composite material shafts made by filament winding method is presented in this paper. The classical laminated plate theory is applied on the patch cut from the composite material hollow shafts. It is verified that the composite material hollow shafts of diameter 40 mm is the most optimum when the ratio of the inner diameter to the outer is 0.4 and winding angle is 45$^{circ}$. It is also proven that the shear strain does not change seriously between 30$^{circ}$and 60$^{circ}$of winding angles. It is dangerous when the winding angle is over 75$^{circ}$because the values of shear strain and stress produced on the shaft are too high so it must be avoided to wind the filament by the angle over 75$^{circ}$.