This paper presents new timing analysis algorithms for efficient state space exploration during timed circuit synthesis. Timed circuits are a class of asynchronous circuits that incorporate explicit timing information in the specification which is used throughout the synthesis procedure to optimize the design. Much of the computational complexity in the synthesis of timed circuits currently is in finding the reachable timed state space. We introduce new algorithms which utilize geometric regions to represent the timed state space and partial orders to minimize the number of regions necessary. These algorithms operate on specifications sufficiently general to describe practical circuits.