AbstractThis paper presents a technique for treating uncertainties in the dynamic models of a structural system. The formulation of the method is presented for a simple case of a single‐degree‐of‐freedom linear oscillator. The uncertainties are modelled as random variables and are assumed to be time‐independent. The solution is expanded as a series involving the random terms, and a system of linear ordinary differential equations for the unknowns of the problem is derived using the weighted residual method. The system of equations is then integrated in time and the response variability is computed. Validation calculations show that the results from the method agree well with those obtained by other solution techniques. Finally, some possible applications and extensions of the present work are discussed.