Abstract: In the report, the existence and stability of the positive solutions for a class of fourth-order ordinary differential equations with three-point boundary value problems were analyzed. Firstly, the properties and estimates of the corresponding Green's function were proposed; secondly, based on these estimates, Krasnosel'skii and Leggett-Williams fixed point theorems were used to discuss the existence of the positive solutions for the fourth-order three-point boundary value problem with a weight function, and the effects of the perturbation term within the different value ranges on the existence of one, two, and three solutions were also considered; thirdly, the Ulam-Hyers stability of the solutions under specific perturbations was systematically analyzed; finally, the numerical simulations were performed to verify the reasonableness and practical value of the proposed results, and which demonstrated the importance and effectiveness of the theoretical analysis in practical applications.