Abstarct: In this thesis an analytical solution for non-axisymmetric heat transfer in multilxayer solid composite cylinder with considering Cattaneo theory is presented. Equation of temperature distribution of this cylinder is solved by separation of variables. Then the effects of lixnk defects between laxyers is investigated and the heat transfer equation for materials that don’t have any complete lixnk is solved and effects of this defects is examined in temperature distribution figures. For more verification the problem solved with numerical method (FEM). Interference of heat waves among the laxyers is investigated. The effect of yarns angle in radial and peripheral directions is examined. At the end the effect of time consideration shows that temperature distribution has the oscillatory behavior. Because of initial condition that is oscillatory too it is possible that the temperature distribution don’t approach to Fourier form before steady state. The temperature distribution in different times is examined.