A common approach for the quantitative analysis of a generalized stochastic Petri net (GSPN) is to generate its entire state space and then solve the corresponding continuous--time Markov chain (CTMC) numerically. This analysis often suffers from two major problems: the state space explosion and the stiffness of the CTMC. In this paper we present parallel algorithms for shared--memory machines that attempt to alleviate both of these difficulties: the large main memory capacity of a multiprocessor can be utilized and long computation times are reduced by efficient parallelization. The algorithms comprise both CTMC construction and numerical steady--state solution. We give experimental results obtained with a Convex SPP1600 shared--memory multiprocessor that show the behavior of the algorithms and the parallel speedups obtained.