Buried land mines, which are triggered by pressure, particularly anti-personnel mines which are triggered by the pressure of a person's foot, are destroyed by impinging laser beam pulses on the surface of the soil. With appropriately chosen beam parameters, a laser supported detonation is created in the atmosphere above the soil by each beam pulse impingement. That results in a blast wave within the soil, the pressure of which causes a mine trigger to explode the mine. A multiplicity of beam pulses are impinged on the soil surface in location- and time-coordination, to create a multiplicity of blast waves which provide pressure-time profiles within the shallow depth of the soil, sufficient to trigger mine types that are configured to resist triggering from a single detonation, whether induced by laser or chemical means.