Metallic nanolayered composite materials can exhibit yield strengths one and a half to two times that of the constituents from which they are constructed. However, experimental data frequently show that there is a critical bi-layer period Λ below which the strength no longer increases with decreasing Λ To help understand the origins of this behavior and to guide future design of multilayers, maps of the internal stress and overall tensile macroyield stress are calculated as functions of the volume fractions of the two alternating constituents and bi-layer period, for a given lattice parameter ratio and elastic modulus ratio. Adopted here is a premise suggested by embedded atom simulations of Cu/Nb multilayers and recent experimental work on γ -Ni/γ-Ni3Al multilayers that the overall tensile strength is determined by the applied stress needed to eliminate the compressive bi-axial stress in the alternating layers. The results indicate that indeed, there is a critical bi-layer period below which the strength is independent of bi-layer period. In this regime, multilayer tensile strength is most effectively improved by increasing the stored compressive stress. This is achieved by decreasing the volume fraction of the compressively stressed phase. This manuscript extends previous work by providing closed-form expressions for the macroyield strength of free-standing multilayered thin films.