The buckling behavior of multilayer shells is studied for composite structures subjected to combinations of uniform temperature change, applied external pressure, and applied and reactive circumferential edge loads. A stability criterion is established for the class of structures of interest and a transverse loading parameter is identified. Critical parameters are identified, and closed form analytical solutions are obtained for the associated non-linear problems. Numerical simulations, based on these solutions, are performed and the stability criterion is applied, revealing characteristic behavior of the structures of interest. Such behavior includes “sling-shot” buckling, whereby the structure slings from deflections in one direction to deflections in the opposite sense, in an unstable manner, at critical temperatures. The influence of external pressure on the critical temperature change of thermally loaded composite structures is elucidated, as is the influence of temperature change on the buckling behavior of pressure loaded multilayer shells.