Observing the locomotion of worms one recognizes a conversion of (mostly periodic) internally driven motions into change of external position (undulatory locomotion). In this paper motion of a system of two material points $x_1$ and $x_2$ with the masses $m$, connected by a spring of stiffness $c$ along an axis $x$ is considered. It is supposed that the points are under the action of a small non-symmetric Coulomb dry frictional force $\varepsilon mF (\dot{x}),\:\varepsilon\ll 1$, depending on velocities $\dot x=\dot{x}_i\, (i=1,2)$, where $F(\dot{x})=F_+$ if $\dot x>0,\:$, $F(\dot{x})=F_-$ if $\dot x<0;\:-F_-\ge F_+\ge 0$. Excitation is carried out by the action of small internal periodic force. Investigations show: at presence of excitation and non- symmetric Coulomb dry friction a motion of the system with a constant on the average velocity $V>0$ is possible and this motion is stable. The expression for $V$ is obtained. A worm prototype applying the principles outlined above has been constructed.