Abstract-Under analysis is travel of P-waves in an elastic pipe partly embedded in soil with dry friction. The mathematical formulation of the problem on impact pipe driving in soil is based on the model of axial vibration of an elastic bar, considering lateral resistance described using the law of solid dry friction. The author solves problems on axial load on pipe in interaction with external elastic medium, and compares the analytical and numerical results obtained with and without accounting for the external medium deformability.Keywords: Axial waves, elastic bar, dry friction, pulsed loading, numerical modelingThe problems on the behavior of pipes in soil appear in many engineering procedures such as driving and pulling of piles, trenchless laying of underground utilities, underground pipework laying. Motion of various rods in mechanical systems always goes with friction. It is important to understand the influence exerted on wave process by friction of external environment and side surface of a pipe or a rod. Research of the interaction of bodies with friction is extensive .The wave processes in rods embedded in a medium were first considered by Gersevanov [11] in 1930, based on Saint-Venant's theory. Later on, propagation of P-waves in a rod with constantamplitude and different-oriented dry friction was an object of study [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. These studies assumed the rod was driven in undeformable medium. A general approach to solving such problems is reducing the nonlinear problem to a set of successively solved linear problems. It is required to define boundaries in time and axial coordinate for domains where friction has constant value and orientation. The axis of friction depends on the sign of the wave velocity. Solution in each of the domains is constructed considering the preliminary determined sign of the velocity. This approach allowed solving a lot of problems with sufficiently simple laws of loading exerted on the rod.Nonstationary and stationary one-dimensional problems on pipe and soil interaction by the law of external dry friction in the framework of the model of sonic and ultrasonic flow of a finite and infinite rod can be found in [8,13,15], and two-dimensional problem of pipe driving in soil is discussed in [19].Many researches focused on problems on piling [26][27][28][29][30][31][32][33][34][35]. In [26] experimental data on hammer accelerations are used to calculate distribution of soil resistance along a pile. In [27] a simple dynamic model is offered to find soil resistance coefficient in the course of piling; the calculated results are compared with the dynamic testing database, and it is discussed how to use the soil resistance model in the wave equation of the pile motion. Dynamic analysis of side surface of pile uses boundary element approach in [28], and the finite element method is chosen to solve axially symmetric twodimensional problem on piling, with algorithm of slip friction contact on the pile and soil interface in [...