The paper is devoted to the problem of delay-independent stability for a class of nonlinear mechanical systems. Mechanical systems with linear velocity forces and essentially nonlinear positional ones are studied. It is assumed that there is a delay in the positional forces. With the aid of the decomposition method and original constructions of Lyapunov–Krasovskii functionals, conditions are found under which the trivial equilibrium positions of the considered systems are asymptotically stable for any constant nonnegative delay. An example is given to demonstrate the effectiveness of the obtained results.