In this paper I construct theoretic search model of the apartment swap in the rental market. With the model, using random matching mechanism, I am trying to mimic Swedish swap market, characterized by the strong rent controls and dominant ownership of the apartments by the municipalities. Proposed theoretic framework is intended to capture supply and demand dynamics of the rental market, segmented to households with rented small or big municipal apartments, that search and try to swap between each other. The paper consider comparative statics of the apartment swap model and try to extract some stylized facts. For that purpose, I have simulated value of the swap itself as the function of the structure of the population, to test the changes in the modeled value of the swap, while varying for the parameters of interest rate, probabilities of match and probability of cancel of the swap agreement. Simulation results have confirmed intuitive expectation from the theoretical postulation.