Pressure-related deep tissue injury (DTI) is a life-risking form of pressure ulcers threatening immobilized and neurologically impaired patients. In DTI, necrosis of muscle and enveloping adipose tissues occurs under intact skin, owing to prolonged compression by bony prominences. Modeling the process of DTI in the buttocks requires knowledge on viscoelastic mechanical properties of the white adipose tissue covering the gluteus muscles. However, this information is missing in the literature. Our major objectives in this study were therefore to (i) measure short-term and long-term aggregate moduli of adipose tissue covering the glutei of sheep, (ii) determine the effects of preconditioning on and , and (iii) determine the time course of stress relaxation in terms of the transient aggregate modulus in nonpreconditioned (NPC) and preconditioned (PC) tissues. We tested 20 fresh tissue specimens (from 20 mature animals) in vitro: 10 specimens in confined compression for obtaining the complete response to a ramp-and-hold protocol (ramp rate of ), and 10 other specimens in swift indentations for obtaining comparable short-term elastic moduli at higher ramp rates . We found that in confined compression were and for the NPC and PC specimens, respectively. The property, , was not affected by preconditioning. The transient aggregate modulus always reached the plateau phase (less than 10% difference between and ) within , which is substantially shorter than the times for DTI onset reported in previous animal studies. The short-term elastic moduli at high indentation rates were and for the NPC and PC test conditions, respectively. Given a Poisson’s ratio of 0.495, comparison of short-term elastic moduli between the high and slow rate tests indicated a strong deformation-rate dependency. The most relevant property for modeling adipose tissue as related to DTI is found to be , which is conveniently unaffected by preconditioning. The mechanical characteristics of white adipose tissue provided herein are useful for analytical as well as numerical models of DTI, which are essential for understanding this serious malady.