Abstarct: In this thesis, an exact solution for conductive heat transfer in cylindrical composite laminates is presented. This analytical solution can be used to analyze the conductive heat transfer, thermal stresses and strains in composite pipes and vessels. The fibers are wounded around the cylinder and the direction of fibers in each lamina can be differed from another laxyers. we focus on axisymmetric heat transfer in cylindrical composite laminates by considering the heat conduction in longitudinal and radial dimensions . This analytical solution is also obtained for general linear thermal boundary conditions which covers combined effect of the heat conduction, convection and radiation at boundaries. Finding the most generalized analytical solution baxsed on the complicated boundary conditions is one of the main innovation of current work. For solving the steady state problem, an appropriate Fourier transformation has been derived using the Sturm-Liouville theorem. We used this Fourier transformation to change the partial differential equation of heat transfer in cylindrical composite laminates to an ordinary equation. Due to the difference of the fibers direction in each laxyer, a set of equations of Fourier series coefficients is obtained baxsed on the boundary conditions at inner and outer of the cylindrical laminate and temperature and heat flux continuity at boundaries located between the laxyers. The solution of these equations is obtained using the recessive Thomas algorithm. In other to solve the problem in unsteady state, we applied the Laplace operator on energy equation and then use the Sturm-Liouville theorem to achieve the solution of obtained equation. Regarding to complicated achieved integral, We use a method named Meromorphic Function to obtain the inverse Laplace transformation.