A mathematical model of transformable gas permeable blasting shelter made from worn out tires of heavy trucks bound together with chains, ropes or cables is proposed. Large displacements and unilateral constraints are specific features of this model. An algorithm was developed to calculate the displacements of tires and internal forces in connecting elements of blasting shelter subjected to dynamic loading. The results of the numerical simulation of simple shelter are presented for assessment of the adequacy of the mathematical model. This algorithm can be used to determine the parameters of shelter such as mass, number of tires, diameter of connecting elements which ensure its safe operation under any sequence of explosions.