In order to study correcting capabilities for figure errors of ultra-thin mirrors with active supports, a 0.5 m demonstration mirror is designed and tested.Firstly, the relevant relations between actuator forces and figure forms are analyzed, and some lower-order figure errors, such as primary spherical aberration, coma, astigmatism and distortion due to gravity, are introduced.Then, the optimization objective is set up, and the Sequential Quadratic Programming (SQP) method for nonlinear constraint problem is applied to calculating optimum actuator forces.The residual figure errors of the ultra-thin mirror are given.Simulation analysis shows that by using the actuator arrangement proposed in this paper,the normalized primary spherical aberration, coma, astigmatism as well as their summation can be corrected to be less than λ/24 rms,and the correcting capability for astigmatism is the strongest and for spherical aberration and coma are less; moreover,the deformation due to gravity combined with the summation of above three lower-order aberrations can also be corrected to be less than λ/24 rms.After the actual surface errors from the interferometry based on the 0.5 m demonstration mirror are given, the optimum actuator forces and form errors are solved.The results show that the surface quality is about λ/7 rms ,which is in accord with the test data.The causes that the figure error can not meet the desired objective are analyzed,then an improved method is proposed.By the method, the figure error of the 0.5 m ultra-thin mirror with active supports satisfies the requirements equal to or less than λ/20 rms.