The paper presents the maximum strength/stiffness design of tension/compression and flexural members under the influence of their self-weight as well as given external forces. In the maximum strength design, all cross sections of the member attain the maximum allowable stress for the material; the design is therefore also referred to as the uniform or constant maximum strength design. In the maximum stiffness design, the maximum longitudinal or transverse displacement is minimized. It is assumed that the location of the maximum displacement is known. In this sense, the paper considers only strict minimization problems. In several cases analytical solutions are obtained. Where this was not possible, solutions derived by successive approximation are given. The variational problem corresponding to this optimization problem has several unique features which are not commonly encountered in the absence of self-weight.