Cranes are underactuated mechanical systems with fewer control inputs than the degrees of freedom. Their usual performance goal is to execute a desired load trajectory, which is specified by as many outputs as the control inputs. A solution to the inverse simulation problem, in which the control of the underactuated system required to execute the partly specified motion is determined, is a challenging task. The inverse simulation study is usually formulated in independent variables. In this paper a dependent variable formulation is reported, advantageous in many aspects. The resultant governing equations appear as simple index-three differential-algebraic equations, and an effective numerical code for their solution is discussed.