This paper investigates the application of a polynomial abductive network modeling technique to a class of hydraulic actuation systems used in heavy-duty mobile machines. Previous techniques to model and simulate heavy-duty hydraulic functions include using a combination of analytical, numerical and steady state solutions in a partitioned hierarchical manner [N. Sepehri, P. D. Lawrence and F. Sassani, Proc. IASTED Int. Conf. on Modeling and Simulation, pp. 170–174 (1991)] or, a transmission line modeling approach to facilitate parallel processing [J. D. Burton, K. A. Edge and C. R. Burrows, ASME J. Dynamic Systems, Measurement and Control 116, 137–145 (1994)]. Using the results from the application of these methods to an excavator-based machine, databases are developed which are then used to construct polynomial abductive network models in order to replace the conventional iterative derivations for fluid flow distribution among the actuators. The networks are generated using a mechanism based on a hybrid learning logic called “abductory induction” [G. J. Montgomery and K. C. Drake, Proc. SPIE—Int. Soc. Optical Engng, pp. 56–64 (1990)]. The performance of the polynomial abductive network model is compared to the previously established model. It is shown that the computation time is reduced considerably, yet the simulation results show a sufficient degree of predictive accuracy. Additionally, the new modeling scheme eliminates the need for explicit derivations of the main valve orifice areas, and therefore facilitates the use of experimental observations in developing simulation models.