An approach to constrained nonlinear lumping for dimension reduction of chemical kinetic models is presented. The approach combines general symbolic methods of nonlinear lumping and numerical techniques to arrive at an analytically reduced model in practical applications of homogeneous kinetic systems. This method can be applied to any first- and second-order reaction system with arbitrary complexity. An H-2/O-2 oxidation model is used as an example for illustrating this method. The resultant lumped models given by modified first- and second-order approximations of nonlinear lumping have very good accuracy for the temperature and all the species. The modified second-order approximation can be applied to arbitrary initial conditions, but the formula is quite complicated. The modified first-order approximation has a simple form, but two empirical parameters need to be determined for a given initial condition.