The stability analysis of a curved sandwich beam with isotropic skins and flexible core is investigated in this research. Derivation of equations for face sheets is accomplished via the classical theory of curved beam, whereas for the flexible core, the elasticity equations in polar coordinates are implemented. The beam construction consists of two skins (not necessarily identical), metallic or composite laminated symmetric, and a soft core made of foam or a low-strength honeycomb that is flexible in the vertical direction. Employing the von-Karman type geometrical non-linearity in strain-displacement relations, nonlinear governing equations are resulted. Linear pre-buckling analysis is performed neglecting the rotation effects in pre-buckling state. Stability equations are concluded based on the adjacent equilibrium criterion. Considering the movable simply supported type of boundary conditions, suitable trigonometric solutions are adopted which satisfy the assumed edge conditions. The critical uniform load of the beam is obtained as a closed-form solution. Numerical results cover the effects of various parameters on the critical buckling load of the beam. To the best of the authors' knowledge, this research is investigated here in for the first time.