The phenomenon of elastic follow-up in high temperature piping has a long history and rules to limit its significance in design are well established. However, most design rules, and numerous associated supporting studies, have been limited to a simple power-law of creep, with variations to account for time- or strain-hardening in primary creep. A common feature of the most studies of elastic follow-up in structures subject to power-law creep is that a plot of (maximum) stress against strain—a so-called isochronous stress– strain trajectory—is almost insensitive to the creep law (in particular, the stress exponent in the power-law) and is almost linear (until perhaps the later stages of stress relaxation). A limitation of the power-law is that it assumes to be valid across all stress ranges, from low through moderate to high, yet it is well known that this is not generally the case. This paper aims to investigate the effect of stress-range dependent material models on the nature of elastic follow-up: both a simple two-bar structure (common in studies of elastic follow-up) and a detailed finite element analysis of a piping elbow are examined. It is found that stress-range dependent material models can have a significant effect on the accepted characteristics of elastic follow-up.