The constitutive parameters of materials can effectively reflect their mechanical properties in relevant service environments, which usually require corresponding mechanical testing methods to obtain. Existing macroscopic mechanical testing techniques necessitate that samples be processed into specific shapes and sizes, whereas the indentation method allows for in-situ testing with simple sample preparation. To effectively obtain the mechanical parameters of metals through indentation testing, this study employed an Instron universal testing machine to conduct quasi-static spherical indentation tests on copper and low-carbon steel. By analyzing the indentation load-depth curves and utilizing a trained neural network, the plastic constitutive parameters of the two metals were inverted and compared with those obtained from tensile tests. The results show that the yield strength of copper based on the neural network and spherical indentation testing is 307.6 MPa, the strain hardening coefficient is 69.7 MPa, and the strain hardening exponent is 0.338 1. For low-carbon steel, the yield strength is 269.4 MPa, the strain hardening coefficient is 541.4 MPa, and the strain hardening exponent is 0.474 3. The maximum relative error between these values and the corresponding results obtained from tensile tests is only 4.22%, indicating the effectiveness of the inversion method of metal plastic parameters based on neural networks and spherical indentation testing. The relevant research of this article can provide a reference method for effectively obtaining the mechanical performance parameters of metals or alloys.