Multistaircase spiral phase plates (SPPs) are more commonly used to generate an optical vortex, as compared to ideal continuous surface SPPs. However, due to the complexities and difficulties involved in the manufacturing of the multistaircase SPPs, the number of the staircases M should not be high and should be sufficient to guarantee a similarity between the M staircase situation (considering an intrinsic topological charge l) and the ideal situation. Therefore, a Fraunhofer diffraction analysis model is proposed to quantitatively and quantificationally solve the diffraction field of the vortex generated by multistaircase SPPs. A finite hypergeometric series summation is applied to solve the diffraction fields of the vortices with different parameters, under the conditions of uniform and Gaussian incident beams. The simulation results show that the summation of the first certain terms of the Fourier expansions can appropriately approximate the diffraction field, and M is positively related with l to approach the ideal situations. Thus, the proposed model can provide a reference for designing and setting the parameters of multistaircase SPPs.