In the article the model of the market with the transaction costs is considered with the market participant who intends to sell the shares of the stock with the presence of the liquidity shortage. The shortage in the liquidity can manfest itself in the occurrence of the market impact which can siginficantly decrease the profit from the stock trade. If the trading velocity is above some level, the market impact can occure and increase the cost of the trade. However the transaction cost can be present even in case of a small transaction on the stock market. The problem of maximization of the expected amount of money obtained from the sale of the stock shares is solved for the case of strategies with the constant trade speed and the particular range of the stock price drift. The example of numerical computations with the use the formulas from the paper, is included.