This paper presents a comparative study of the Explicit Optimal Design methods (EOD) applied to the design of elastic trusses under multiple loading conditions. The EOD method is a technique which allows to formulate a structural optimization problem in a mathematical programming form where the objective function and the stress and displacement constraints are explicit functions of the design variables. This is obtained by choosing as design variables a convenient subset of the cross-sectional areas and stresses of the truss elements and the nodal displacements. The selection of the subset determines the type of the EOD method used, namely the Force EOD method, the Displacement EOD method or the Hybrid EOD method. The implementation of the EOD method in the case of multiple loading conditions causes an expansion of the dimensionality of the design space since the behavioral variables, stresses and displacements must be duplicated for all loading cases. This necessitates in turn the addition of equality constraints to the design formulation. The objective of this study is to evaluate the implications of the expanded design space and additional constraints on the feasibility of the EOD approach. Likewise this paper compares the three EOD methods in the context of multiple loading conditions with a view of establishing their relative advantages. The minimization process is carried out using a sequence of unconstrained minimization algorithms in conjunction with a 'moving' external penalty function. The approach is illustrated with examples of truss designs taken from the literature. The numerical results indicate that the method can favorably be applied to medium size problems especially in the case of the Force EOD approach.