We investigate variants of Goddard's problems for nonvertical tra- jectories. The control is the thrust force, and the ob jective is to max imize a certain final cost, typically, the final mass. In this article, performing an analysis based on the Pontryagin Maximum Principle, we prove that optimal tra jectories may involve singular arcs (along which the norm of the thrust is neither zero nor maximal), that are computed and characterized. Numerical simulations are carried out, both with direct and indirect methods, demonstrating the relevance of taking into account singular arcs in the control strategy. The indirect method we use is based on our previous theoretical analysis and consists in combining a shooting method with an homotopic method. The homotopic approach leads to a quadratic regularization of the problem and is a way to tackle with the problem of nonsmoothness of the optimal control.