The paper presents the analysis of buckling and initial postbuckling behavior of long cylindrical sandwich shells subjected to a lateral pressure. The shells considered in the paper have dissimilar facings reflecting a demand to enhance impact resistance and damage tolerance of the facing exposed to external loads and hostile environments that are typical in applications. The shell being long, its central section remains in the state of plane strain prior to and after buckling. The solution includes the analysis of prebuckling deformations and linear and nonlinear buckling problems. It is shown that prebuckling deformations affect postbuckling shell behavior but they do not affect the linear (upper) buckling pressure. Numerical results presented in the paper illustrate that a moderate redistribution of the layers between the facings results in a limited reduction of the buckling pressure compared to the case of symmetric facings.