This paper extends the Monte Carlo technique to systems that exhibit non-parametric uncertainty, i.e. when the form of the equations is not known exactly. A large number of monotonic curves are generated randomly within the envelopes that bound the incompletely known functions. Each generated curve is substituted into the ODEs that describe the system, which are integrated to determine trajectories of the state variables. To ensure a satisfactory coverage of the space of monotonic functions, a recursive-subdivision algorithm is introduced for discretization of the independent variables, with the dependent variable randomly selected at each grid point, according to suggested distributions. The technique is applied to verify the stability of closed-loop nonlinear systems, as arise in chemical plants with process controllers.