:In this thesis unilateral buckling of circular cylindrical isotropic homogenous and composite laminated panels with finite curvature radius on tensionless elastic foundation excited by in plane mechanical and thermal loads is analyzed with Rayleigh-Ritz method. Stability analysis governing equations are extracted based on classic theory assumptions and using Sanders strain-displacement relations and applying virtual work principle on total potential energy equation. In applying thermal loads it is assumed that the panel is in isothermal heat exchange with its environment. So energy equation is written based on mechanical effects and the influence of uniformly distributed temperature arise is introduced to the equations as initial stresses. For defining the distribution of in plane loads resulted from thermal forces, static analysis is done before stability analysis. So governing equations are presented with two pre-buckling static analysis equations and one linear buckling analysis equation.In this thesis a net consisting of concentrated springs are used to simulate the foundation and because of the bi-modulus behavior of foundation in the presence of compression and tensional forces in contact area between panel and foundation, a contact function is used. Elastic buckling curves of homogenous isotropic and composite laminated circular cylindrical panels excited by in plane mechanical and thermals loads are presented.These curves show the relation between critical buckling and critical thermal loads with length to perimeter ratio in a specific central angle of panel and the relation between critical buckling load and temperature with central angle.Besides the effect of number and arrangement of layers in constant thickness, length to perimeter ratio, radius to thickness ratio, boundary condition, fibers orientation on critical buckling and temperature of unilateral and bilateral buckling is investigated. For verifying the present method unilateral buckling of a panel with infinite curvature radius is compared with previous work. Results have shown that the increase in the panel area because of the rise in length to perimeter ratio will not necessarily lead to the increase in the contact area between panel and foundation and as a result the critical buckling load. it is abserved that by decreasing in the radiys to thickness ratio, on contrary to rise incritical load and temperature, the influence of the unilateral constraint on the critical load and temperature will decline. Besides by increasing the number of layers in constant thickness the influence of unilateral constraint decreases. keywords: stability analysis, bilateral buckling, unilateral buckling, Rayleigh-Ritz method, classic theory, elastic foundation,cylindrical panels.