The paper is concerned with wrinkling of thin facings in sandwich structures with a bi-modular elastic core. Bi-modularity of core implies a different stiffness in tension and compression. The solution to the wrinkling problem is obtained by an extension of the Hoff method. One of two bounding cases are the classical Hoff solution where the stiffness of the core in tension is equal to that in compression. In the second case demonstrated in the paper the mismatch in the stiffness of the core in tension and compression is so large that the higher stiffness can be assumed infinite. The solution for intermediate cases where the ratio of the core stiffness in tension to that in compression is finite is also presented in the paper. In addition, the approach to the analysis of wrinkling utilizing the stresses in the core derived by the theory of elasticity is discussed and the closed-form solution obtained in the particular case of equal tensile and compressive moduli. It is shown that a mismatch in the elastic moduli of the core in tension and compression results in the change in the mode shape of wrinkling as compared to the core with equal tensile and compressive stiffness. An increase in the stiffness of the facing or using a stiffer bi-modular core results in a higher wrinkling stress. It is also demonstrated that a higher stiffness of a bi-modular core in either tension or compression causes only a limited reduction in the energy absorbed prior to wrinkling.