The corresponding nonlinear differential equation with the effect of dead loads taken into account is formulated from Hamilton principle. Based on the equation, the effect of key physical factors, including the magnitude of dead loads, the height and span of the arch beam, the moment of inertia and the radius of inertia, etc, on natural frequencies of the arch beam, are discussed by using Galerkin method. It is shown that the existence of dead loads raised the natural frequencies of arch beams, and the differential equations can be applied to both arch and straight beams. The varying deterrent effect of dead loads relates to the magnitude of dead loads and the stiffness of structures. The effect is more apparent for flexible structures and at lower natural frequencies.