An apparatus has been designed and constructed that will allow determination of the mechanical behavior of polymer specimens subject to applied tensile and compressive loading, while the sample is simultaneously subject to a hydrostatic pressure environment. The moduli of high‐density polyethylene and polypropylene determined from compressive tests show a significant increase with pressure. Tensile nominal stress‐strain curves have been obtained at various pressures up to 100 000 psi. These show that the yield stress also increases significantly with increasing pressure for both materials. The nature of yielding and fracture is found to be quite different for the two polymers studied. Polyethylene tends to deform more by shear, and the necked region at high pressures reduces to a fine point before separation. In polypropylene, fracture occurs by plastic tearing across the cross section. An attempt is made to account for the experimental results by use of yield criteria that includes a hydrostatic pressure component. Consideration is also given to the effect of finite deformation theory on the increase in modulus of elasticity under a high pressure environment. The specific nature of the effects produced by the high pressure is found to depend strongly on the molecular structure of the polymer.