First-order shear deformation theories, one proposed by Reissner and another one by Mindlin, are widely in use, even today, because of their simplicity. In this paper, two new displacement based first-order shear deformation theories involving only two unknown functions, as against three functions in case of Reissner’s and Mindlin’s theories, are introduced. For static problems, governing equations of one of the proposed theories are uncoupled. And for dynamic problems, governing equations of one of the theories are only inertially coupled, whereas those of the other theory are only elastically coupled. Both the theories are variationally consistent. The effectiveness of the theories is brought out through illustrative examples. One of the theories has striking similarity with classical plate theory.