(1) Background: A tophus is a clinical manifestation of advanced gout, and in some patients could lead to joint deformities, fractures, and even serious complications in unusual sites. Therefore, to explore the factors related to the occurrence of tophi and establish a prediction model is clinically significant. (2) Objective: to study the occurrence of tophi in patients with gout and to construct a predictive model to evaluate its predictive efficacy. (3) Methods: The clinical data of 702 gout patients were analyzed by using cross-sectional data of North Sichuan Medical College. The least absolute shrinkage and selection operator (LASSO) and multivariate logistic regression were used to analyze predictors. Multiple machine learning (ML) classification models are integrated to analyze and identify the optimal model, and Shapley Additive exPlanations (SHAP) interpretation was developed for personalized risk assessment. (4) Results: Compliance of urate-lowering therapy (ULT), Body Mass Index (BMI), course of disease, annual attack frequency, polyjoint involvement, history of drinking, family history of gout, estimated glomerular filtration rate (eGFR), and erythrocyte sedimentation rate (ESR) were the predictors of the occurrence of tophi. Logistic classification model was the optimal model, test set area under curve (AUC) (95% confidence interval, CI): 0.888 (0.839–0.937), accuracy: 0.763, sensitivity: 0.852, and specificity: 0.803. (5) Conclusions: We constructed a logistic regression model and explained it with the SHAP method, providing evidence for preventing tophus and guidance for individual treatment of different patients.