Background: Fastest mean (MVfastest) and peak (PVfastest) velocity of the set have been proposed to predict the maximum number of repetitions to failure (RTF) during the Smith machine prone bench pull (PBP) exercise. Hypothesis: Goodness-of-fit would be higher for individualized compared with generalized RTF-velocity relationships and comparable for both execution equipment conditions (with or without straps), and the MVfastest and PVfastest associated with each RTF would be comparable between execution equipment and prediction methods (multiple- vs 2-point method). Study Design: Cross-sectional study. Level of Evidence: Level 3. Methods: After determining the PBP 1-repetition maximum (1RM), 20 resistance-trained male athletes performed 2 sessions randomly, with and without lifting straps, consisting of single sets to failure against the same load sequence (60% to 80% to 70% 1RM). Generalized (pooling data from all subjects) and individualized (separately for each subject using multiple-point or 2-point methods) RTF-velocity relationships were constructed. Results: Individualized RTF-velocity relationships were always stronger than generalized RFT-velocity relationships, but comparable with (MVfastest: r(2) = 0.87-0.99]; PVfastest: r(2) = 0.88-1.00]) and without (MVfastest: r(2) = 0.82-1.00; PVfastest: r(2) = 0.89-0.99]) lifting straps. The velocity values associated with each RTF were comparable between execution equipment (P >= 0.22), but higher for the multiple-point compared with the 2-point method (P < 0.01). Conclusion: The use of lifting straps during the Smith machine PBP exercise does not affect the goodness-of-fit of the RTF-velocity relationships or the velocity values associated with different RTFs. However, caution should be exercised when using different methods.