Phasetype distributions， defined as the distribution of absorption times of certain Markov jump processes， constitute a class of distribution on the positive real axis which seems to strike a balance between generality and tractability.Any positive distribution can be approximated arbitrarily by phasetype distributions.Under the condition that the interclaim times of constant interest is phasetype distribution risk model， some of their basic properties and the precise solution of GerberShiu discounted penalty function are obtained.