It is of great significance to study the deformation characteristics and stress distribution of aortic wall. Reliable prediction of constitutive parameters requires an inverse process, which possesses challenges. This work proposes two inverse procedures to identify the constitutive parameters of aortic walls. The first one integrates nonlinear finite element method (FEM), random forest (RF) model and Bayesian optimization (BO) algorithm. The other one integrates FEM, RF and hybrid Grid Search (GS) and Random Search (RS) algorithm. FEM models are first established to simulate nonlinear deformation of aortic walls subject to uniaxial tension tests. A dataset of nonlinear relationship between the engineering stress and main stretch of aortic walls is created using FEM models and the nonlinear relationship is learned through RF model. The BO, hybrid GS and RS algorithms are used to adjust the major model parameters in RF. Then the optimized RF is utilized to predict constitutive parameters of aortic walls with the help of uniaxial tension tests. Intensive studies also have been carried out to compare the RF-BO approach with RF-Search approach, and the comparison results show that RF-BO approach is an effective and accurate approach to identify the constitutive parameters of aortic walls. The present RF-BO model can be further extended for the predictions of constitutive parameters of other types of nonlinear soft materials.