A new formulation is presented for the analysis of tapered sandwich structures with anisotropic composite faces. Three local coordinate systems are introduced to describe the independent displacements of each component. The expression for the total potential energy is derived and the Rayleigh-Ritz method is applied to obtain an approximate solution. The analysis takes into account the correlation between the core shear strain and the face normal deflection existing only for the tapered geometry. The present formulation can be applied to arbitrary boundary conditions. Numerical examples are calculated for various core shear modulus ratios, taper ratios, and slenderness ratios. The correlation between the core shear strain and the face normal deflection is found to be very important in predicting the deflections and stresses of tapered sandwich structures.