We develop a method for animating systems with open and closed loops and in particular ladder climbing for virtual world applications. Ladder climbing requires the modeling of dynamic open and closed-loop chains. We model the stance phase and the associated closed-loop dynamics, through the use of the Lagrange multiplier method which results in a system of differential algebraic equations (DAE). We use the Lagrange method for the dynamic formulation of the swing phase. The input to the algorithm is a given forward velocity, step length, step frequency and a chosen gait. The algorithm then determines the initial and final positions for each phase of ladder climbing. We use the Newton-Ralphson method to find the vector of joint torques that drives the dynamic system from the initial position to the final position. We use the Baumgarte stabilization method to achieve stability of the numerical integration. We present a series of real-time animations involving ladder climbing.