The effective flexural properties of integral skin foams (ISF), are modeled using Euler-Bernouli beam theory along with a power law empirical equation relating the properties of a homogeneous foam to its density. The optimal density profile that maximizes the effective flexural modulus of an ISF beam of fixed overall density, and with the density constrained to lie in a given range, is continuous when the power law exponent (n) is less than 1. For n > 1, the optimal density profile is discontinuous with a low density core and a high density skin. The effective flexural modulus of such sandwich beams is maximized for a fixed density ratio (ratio of the core density to the skin density) and fixed overall density. The maximal flexural modulus is found to increase monotonically with decreasing density ratios and increasing values of n. The flexural strength of the sandwich beam is also maximized considering failure to occur by tensile fracture or buckling of the skin. In this case an optimal skin thickness and an optimal density ratio are obtained for a fixed overall density. The results are useful for the design and evaluation of flat ISF panels.