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One of the approaches in modeling of electric arc furnace is based on the power balance equation and results in a nonlinear ordinary differential equation. In reality it can be observed that the graph of the arc voltage varies randomly in time, in fact it oscillate with a random time-varying amplitude and a slight shiver. To get a more realistic model, at least one of the model parameters should be modeled as a stochastic process, which leads to a random differential equation.We propose a stochastic model using the stationary Ornstein-Uhlenbeck process for modeling stochastic influences. Results, gained by applying Monte Carlo method and polynomial chaos expansion, are given here.