This paper introduces modeling and its modal analysis procedure for exact and closed form solution of in-plane vibrations of general Timoshenko frame structures using exact dynamic element method(EDEM). The derivation procedure of the exact system dynamic matrices for Timoshenko beam frames is described. A new modal analysis procedure is also proposed since the conventional modal analysis schemes are not adequate for the proposed, exact system dynamic matrix. The proposed method provides exact modal parameters as well as all kinds of closed form solutions for general frame structures. Two numerical examples are presented for validating and illustrating the proposed method. The numerical study proves that the proposed method is useful for dynamic analysis of frame structures.