In this article the killed Markov decision processes for countable models on finite time interval are considered. The existence of a uniform ε-optimal policy is proved. The correctness of the fundamental equation is shown. The optimal control problem is reduced to a similar problem for derived model. Also, the optimality equation and method for simple optimal policies constructing is received. A sufficient condition of simple policies for countable models is proved. The correctness of the Markovian property is shown. Additionally dynamic programming principle is considered.