In this study, the endochronic theory was used to investigate the collapse of thick-walled tubes subjected to external pressure and axial tension. The experimental and theoretical findings of Madhavan et al. (1993) for thick-walled tubes of 304 stainless steel subjected to external pressure and axial tension were compared with the endochronic simulation. Collapse envelopes for various diameter-to-thickness tubes under two different pressure-tension loadings were involved. It has been shown that the experimental results were aptly described by the endochronic approach demonstrated from comparison with the theoretical prediction employed by Madhavan et al. (1993). Furthermore, by using the rate-sensitivity function of the intrinsic time measure proposed by Pan and Chern (1997) in the endochronic theory, our theoretical analysis was extended to investigate the viscoplastic collapse of thick-walled tubes subjected to external pressure and axial tension. It was found that the pressure-tension collapse envelopes are strongly influenced by the strain-rate during axial tension. Due to the hardening of the metal tube of 304 stainless steel under a faster strain-rate during uniaxial tension, the size of the tension-collapse envelope increases.