Carrying capacity plays a meaningful role on the dynamics of population's models as acts as a limit for the growth of population. In this thesis, I study the effect of Variable carrying capacity on a single population and four different prey-predator models, namely prey-predator model with Holling type I func tional response, prey-predator model with Holling type II functional response, prey-predator model with Holling type I functional response incorporating a prey refuge and prey-predator model with Holling type II functional response incor porating a prey refuge. For the single population model, I have considered two types of variable carrying capacity, namely, logistically variable carrying capacity and periodic carrying capacity. I have found that the single population growth follows the curve of the logistic variable carrying capacity and I can see from this model the bi-logistic phenomenon. Moreover, the periodic variable carrying capacity force the solution of single population model to be periodic. In all four prey-predator models, it has been found that when the growth rate of the logistic variable carrying capacity is very small, the periodicity in the solutions of the systems decrease in magnitude and the solutions reach to the stable equilibrium faster than the corresponding systems with constant carrying capacity. Moreover, when a limit cycle exists in Holling II functional response models, the growth rate of the logistic variable carrying capacity when it is very small has the effect of converting the stable limit cycle into a spiral stable equilibrium point.