The purpose of this paper is to formulate an analytical method for investigation for dynamic stability of trussed beams of long span due to vertical earthquake motions and also to express the quantitative earthquake resistant capacity in terms of the first natural period and the slenderness ratio of used upper chord members. The numerical modeling of the structures is shown to be efficient from a view point of computer calculation and has a preciseness for representing the lateral buckling of the upper chord leading to a collapse. The configuration and structural proportioning is designed according to Japanese Design Standard for Steel Structures under an assumption that the lateral buckling of the central upper chord brings about its collapse due to the vertical earthquake motion and its self weight. Varying the slenderness ratio of upper chords for the lateral buckling, the static and dynamic analysis has been performed including the plastic deformation and the parametric study for numerical results leads to the following conclusion : (1) The present trussed beams can endure an earthquake motion having more than 300 gals as its peak acceleration in the case of TAFT UD earthquake. (2) An efficient criteria, effective for a design practice, which can adequately evaluate the earthquake resistant capacity is shown possible to be expressed by several parameters as the first natural period, the factor of safety of the central upper chord against lateral buckling and a ductility parameter inherent to the slenderness ratio of the used member.