In this paper, we consider the risk reserve process with Erlang type claims. 
We make the model that the claim inter-arrival time has an exponential 
distribution and the claim size has an Erlang distribution. 
For this model we obtain a general formula that derives the non-ruin probability
in finite time.
In order to have an easy calculation for the
 non-ruin probability we reduce the multi-summation to the single-summation.