The paper deals with the second order non-smooth dynamical system involving friction term: For \((t_0,q_0,\dot q_0)\in \mathbb R\times \mathbb R^m \times \mathbb R^m\) to find a function \(t\mapsto q(t)\;(t\geq t_0),\;q\in C^1([t_0,+\infty);\mathbb R^m)\;\) such that \[ \begin{aligned} &\frac {d^2q}{dt^2}\in L_{loc}^\infty (t_0,+\infty;\mathbb R^m), \;\frac {dq}{dt}\;\text{is right differentiable},\;(q(t_0),\frac {dq(t}{dt}(t_0))=(q_0,\dot q_0),\\ &M\frac {d^2q}{dt^2}+C\frac {dq}{dt}+\varPi'(q(t))\in -H_1\partial \varPhi (H_1^T\frac {dq}{dt}),\;\text{a.e.}\;t\geq t_0, \end{aligned} \] where \(\varPhi:\mathbb R^l\to \mathbb R,\;\varPi:\mathbb R^m\to \mathbb R,\;C\in \mathbb R^{m\times n},\;H_1\in \mathbb R^{m\times l}\) and \(\partial \varPhi\) denotes the convex subdifferential of \(\varPhi.\;\) Sufficient conditions for the local attractivity of the set of stationary solutions are given in the case of dry friction and negative viscous damping. An estimation of the attraction domain is stated. Applications in unilateral mechanics are explained.