A method for the determination of sufficient conditions for the almost-sure stability of some continuous systems of physical interest is presented. The motions of the systems under consideration are assumed to be described by linear partial-differential equations with time-varying coefficients of a random nature. The method presented, which is of a rather general form, is restricted for the sake of simplicity and ease of computations and is applied to problems of elastic columns and plates, a cantilever beam subjected to a random follower force, and a string excited by a pressure-type random force. The emphasis both in the computations and in the nature of the method is on simplicity of computations and in the determination of stability conditions with a minimum of assumptions.