||On the basis of his economic model Solow has derived a differential equation, whose solution is k=k(t), where k=K/AL (AL is a unit of effective labour), with optional value of initial condition k(0). In this work we have completed a mathematical analysis of the Solow model, i.e. an analysis of properties of the solution of autonomous differential equation dk/dt=F(k), where the function F is determined by the Solow model. It has been proved that within the interval k, exists just one asymptotically stable stationary solution. Further, an upper and lower estimate of the solution of the Solow model has been derived, which for converge to one asymptotically stable stationary solution. That enables us to both estimate the solution k(t) with a desired accuracy and estimate speed of convergence of the solution to asymptotically stable stationary solution. In the economic part of the work are the acquired mathematical conclusions applied mainly on the impact of the saving rate on long run economic growth. Former concepts (higher saving rate generates a higher growth rate of product in the long run) are compared with different conclusions resulting from Solow model.