Strength prediction of materials is an important application of shakedown analysis. Inspired by Dang Van's theory, numerous studies have evaluated endurance limits of materials by direct methods (DMs) based on the Von-Mises or Drucker-Prager yield criterion. It is worth noting that very few researches could implement the Dang Van’s view for shakedown analysis of polycrystalline materials using DMs from the perspective of crystal plasticity (CP). To this end, in the present paper we developed a direct method (CP-DM) for crystal plasticity based shakedown analysis. In this approach, the lower bound theorem is integrated with a crystal plasticity constitutive model, and the CP-DM is constructed based on the strain rate independence and the kinematic hardening of materials. Taking the AlSi10Mg made by laser melting deposition (LMD) as the exemplary material, statistically equivalent representative volume elements (SERVEs) of polycrystals were generated, and crystal plasticity parameters were calibrated by experimental tensile curves. In several case studies, the proposed numerical method was carefully verified by incremental analysis, and the rate-independence of the constitutive model was robustly checked. The verified method was employed to statistically predict the shakedown limits of LMDed AlSi10Mg. This paper confirmed the statistical robustness of the derived results through analyzing the size effect of SERVEs. The numerical method developed in this study can be a promising approach to directly predict shakedown limits of rate-independent polycrystalline materials.