Large containers for liquids, exposed to different static loadings, are mainly made of high-density polyethylene (HDPE). The viscoelastic response of HDPE under long-term tensile and compressive creep is investigated. Monotonic experiments under tension are performed over a wide range of strain rates. In these experiments, the transition in the damage mechanisms (development and propagation of contraction in the HDPE specimen) is analyzed. The monotonic tensile behavior of the HDPE is found to be nonlinear and depends on the strain rates. It is observed that both elastic modulus and plastic flow stress present an increase with displacement speed due to the viscoelastic behavior of HDPE. A similar observation can be made for monotonic compressive tests by developing a new experimental device that ensures accurate measurement of the strain. Such a device makes use of an extensometer of compressive displacement of the specimen. In addition, the long-term behavior of HDPE is evidenced through creep and relaxation tests at an imposed range respectively of lower stresses and strains. It is shown that the normalized curves, associated with these tests, can be represented by a single curve characterizing the compressive creep compliance or relaxation stresses versus time. The linearity of the viscoelastic behavior is confirmed within the linear domain of the monotonic compressive and tensile tests.