Traditional parametric models of solid mechanics have disadvantages such as poor lightweight level of cloud data and low integrity of operations of solid mechanics. To solve the above problems, a parametric model for solid mechanics in engineering research based on cloud computing models is designed. By calculating the number of cloud data copy optimizations, the upper limit of resources required for engineering research is estimated, and the specific values is assessed by continuously cycling the demand, so as to complete the basic conflict analysis, and set up a cloud computing engineering research environment. On this basis, the modeling index is selected. By analyzing the sensitivity of the index, the purpose of optimizing the modeling parameters is achieved, and a new solid mechanics parametric model is constructed. Analyzing and contrasting the experimental data shows that after applying the parametric model of solid mechanics in the engineering research based on the cloud computing model, the lightweight level of cloud data can be increased by up to 24 levels, and the operational integrity of solid mechanics can be increased by about 30%.