The application of Petri nets to analyze and simulate biological pathways has been developed vigorously. Some of the modifications of Petri nets appeared to perform quantitative analysis of biological pathways: hybrid Petri net, timed Petri net, stochastic Petri net and so on. For a quantitative analysis of biological pathways, we propose to adopt Runge-Kutta methods to act on a continuous Petri net. We show that Runge-Kutta methods are applicable to a continuous Petri net in glycolysis and apoptosis pathways with reliable and efficient simulation results.