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We analyse the simple model of economic growth with two kinds of physical capitals: private and public capital. We assume that a producer's decision to increase stock of private capital congest the public capital available for other producers. And the households optimize their utility from consumption in infinite time horizon. This economic growth model with congestion of public capital has the form of a 3-dimensional dynamical system with the rates of private capital, public capital as the model variables. We use the mathematical methods of the dynamical systems theory for analysing dynamics of the model. We find a unique steady-state solution as a saddle point with two-dimensional unstable subspace and one-dimensional stable subspace. The latter contains the saddle trajectory along which the system evolves to the steady-state. The economic system moves on the saddle trajectory towards the saddle where the rates of growth of these state variables are constant and equal $a+n$. We also obtain the optimal rate of tax which maximizes the households consumption in the steady state which is equal of the public capital share in income. The numerical analysis allows us to visualize the phase space of the model in the phase portraits.
