Dynamic responses and bearing capacity of members under blast loadings are directly affected by different boundary restraints. In this paper, both elastic and plastic analytical methods for a beam with general flexible supports and restraints under blast loadings are proposed, and the effects of vertically elastic and damping support, horizontal supporting stiffness, rotational constraint, loading characteristics and the dynamically intensifying coefficient of yielding bending moment on responses are analyzed. The results show that the inertia forces owing to vertically elastic support and damping support can decrease the dynamic coefficient of deflection of the beam markedly in elastic-plastic stages. Horizontal supports, which exert transverse pressure on section during the deformation process, and rotational restraints, which confine the rotation of rigid body directly, both have great effects on dynamic responses mainly in plastic range in terms of reducing the dynamic coefficient of displacement and increasing the resistance of the beam accordingly. On the condition with the same constraints and peak load, the dynamic coefficient of displacement of a beam under rectangular pulse loads is always higher than the one under triangular pulse loads, which implies longer duration of pulse loads is negative for bearing capacity. In addition, potential anti-explosion resistance of beams can be improved by taking intensifying coefficient of yielding bending moment into account.