This paper proposes a new model that generalizes the linear multistate sliding window system to the case of multiple failures. In this model, the system consists of independent linearly ordered multistate elements. Each element can have different states: from complete failure up to perfect functioning. A performance rate is associated with each state. The system fails if, at least in groups of consecutive elements (windows), the sum of the performance rates of elements belonging to the group is less than a minimum allowable level. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of evaluating system reliability and elements' reliability importance indices are presented.