It is a fundamental and classic problem to solve the deformation and internal force of a prismatic multi-span continuous beam with equal spans in the area of civil engineering. Based on the Euler–Bernoulli beam theory, this study firstly derives the analytical expression of the beam-end rotational stiffness of an equal-span prismatic continuous beam consisting of any number of spans by utilizing the displacement method in structural mechanics and auxiliary series in mathematics, and then establishes the analytical formulas for determining the joint rotation and bending moment at the supports of continuous beams subjected to various kinds of static loads and actions, i.e., a single point load applied at mid-span, distributed load applied over the span length, and differential temperature change between the top and bottom surfaces of the beam. It is found that as the number of spans goes infinity, the beam-end rotational stiffness of an equal-span prismatic continuous beams approaches to the upper limit 2sqrt(3) i0, where i0 is the linear stiffness (the product of the modulus of elasticity E and the moment of inertia I divided by the length l0 of the member) of single-span beams. For equal-span prismatic continuous beams with different number of spans, the analytical formulas of the joint rotation and bending moment at the supports have unified expressions, while the difference between formulas for different static loads and actions is solely determined by the fixed-end bending moment of single-span beams. This set of formulas shows the advantages of concise form, general applicability, and convenient calculation. It can reveal the influence of the number of spans on the mechanical characteristics of continuous beams, and can also be used to analyze the real-world engineering problems such as optimization of the launching noses for incrementally launched bridges.