In this article the authors performed linear, nonlinear and numerical analysis of glycemic regulation mathematical model described by two differential equations with one delay argument. The results obtained in the linear analysis were used in numeric analysis while constructing stable periodic solutions applying the Runge–Kuto IV successive method in normal and diabetes cases. Impact of physical exercise on the dynamics of glucose and insulin was modelled as well while introducing two external periodical functions defining diet and physical exercise into the above mentioned model. We applied the simulation modelling program “Model Maker” for modelling.