A mathematical model of the dynamics of insulin and glucose during a frequently sampled intravenous glucose tolerance test (IVGTT) in sheep was developed that characterizes the large second-phase insulin secretion response in sheep during IVGTT. The model was fit to measurements of the glucose and insulin dynamics during standard IVGTT ( = 42) and modified IVGTT ( = 40), where insulin was injected 60 min after the initiation of the IVGTT. The correlation between log insulin sensitivity determined by hyperglycemic clamps (HGC) and standard IVGTT was = 0.43 ( = 0.005). The correlation between log insulin sensitivity determined by HGC and modified IVGTT was = 0.51 ( = 0.002). The model, therefore, provides a method to determine insulin sensitivity through a cheaper and more easily performed IVGTT. We validated our estimation procedure using 2 independent experiments on the effect of 1) pregnancy and 2) being born preterm and exposed to dextrose or dextrose with insulin on HGC-derived insulin sensitivity. The IVGTT-derived insulin sensitivity was significantly greater in pregnant ewes than in prepregnant ewes (difference of 0.39 ± 0.12 log n ng mL; < 0.05), and this was consistent with the significantly greater hyperinsulinemic euglycemic clamp-derived insulin sensitivity in pregnant ewes than in prepregnant ewes (difference of 4.03 ± 0.66 µmol mL kg min ng; < 0.001). There was no significant effect of being born preterm on IVGTT/HGC-derived insulin sensitivity. Basal insulin, insulin sensitivity, insulin production, and insulin clearance were lower in prepregnant ewes ( < 0.05). That is, prepregnant ewes have a lower insulin equilibrium status and less responsive insulin turnover. There was also a significant effect of insulin therapy on the rate of insulin clearance in preterm lambs ( < 0.05). This effect was independently significant of its covariance with all other model parameters. Therefore, it can be interpreted as a direct effect on the rate of insulin clearance by the insulin treatment. All other parameter responses to the insulin treatment effect can be regarded as being due to the covariance between these parameters. These analyses demonstrate that treatment effects on insulin sensitivity can be detected using IVGTT experiments.