This paper presents the study of the viscoelastic behavior of high-density polyethylene (HDPE) ASTM 4710 pipes under diametral loads. The experimental procedure consists of applying a displacement ramp followed by a stress relaxation stage on six ring specimens extracted from pipes with varying thickness-to-diameter ratios. The proposed methodology combines the Standard Linear Solid Model (SLSM) with beam theory, introduces adjustment equations for estimating SLSM parameters, and discusses the influence of residual stresses induced during pipe manufacturing and cooling. Finally, the paper shows the validation of the modeling approach based on the results of the mechanical response of an independent test case.