This paper is further development of the nonlinear vibro- acoustic technique, first presented at the previous SPIE conference on Detection and Remediation Technologies for Mines and Mineline Targets, Orlando '98. The present paper discusses the physical/mathematical model and experimental result of detection and discrimination of buried land mines. The mathematical model based on simplified 'mass-spring' approach. The effective spring has a nonlinear stiffness due to a nonlinear boundary condition at the soil-mine interface. Resulting nonlinear equation of motion and its solution in a good agreement with experimental observations. It has been demonstrated numerically and experimentally, that dynamically compliant mine cases exhibit strong nonlinear acoustic response, while less compliant false targets, such as rocks, solid pieces of wood and steel, and etc., behave as dynamically linear systems. The discovered nonlinear phenomenon has been used to develop the nonlinear vibro-acoustic method for land mine detection and discrimination. The experimental studies were performed with real inert plastic and wooden mines under laboratory and field conditions. First, the detection was performed with a contact sensor. Later, the method was tested using remote senors, such as a laser-doppler vibrometer and specially developed microwave vibrometers. These remote sensor demonstrated applicability for the developed nonlinear technique.