A worst-case impact is an external disturbance or force applied to the system that leads to the most adverse or undesirable outcome, such as maximum displacement, failure, or significant deviation from the desired state. The article is devoted to finding the worst disturbance acting on a linear system (for the convenience of result interpretation, mechanical systems are considered) for three classes of functions, namely: classes \(L_2\) , \(L_{\infty }\) and \(L_1\) . The problems of finding the worst-case disturbances are considered over a finite period of time. Explicit formulas are given for the obtained worst-case disturbances, as well as for the system performance indices. Examples of solving worst-case disturbance problems for a single-mass mechanical system and a multi-mass mechanical system, which is a homogeneous chain of elastically connected material points, are given.