•The error sources of inaccurate initial stiffness of self-centering braces are determined.•Parametric studies are conducted to study the effects of fabrication tolerances.•A prediction equation is proposed for estimating the reduced axial stiffness.•Stiffness prediction accuracy using the proposed equation is experimentally validated. The self-centering energy dissipation (SCED) brace is an innovative structural component of seismic-resistant systems that provides a flag-shaped response with good energy dissipation and self-centering capacity. The initial stiffness of the SCED brace is a crucial parameter for brace design and a braced frame system. The current use of SCED braces is limited by the significant discrepancy between the actual and theoretically predicted initial stiffnesses. In this paper, the sources resulting in the inaccurate prediction are identified as the accuracy of the theoretical governing equations and the practical fabrication tolerances of the braces. The accuracies of the governing equations with different levels of complexity are analyzed and compared based on a typical SCED brace. To investigate the reduction effect of fabrication tolerances on the effective axial stiffness, a large number of numerical simulations are conducted on an axially loaded tube member with different tolerance characteristics, including the fundamental length tolerance, contact surface nonuniformity, and load level. According to the trends of the effective axial stiffness, a valid stiffness reduction factor is defined. It can provide good estimates of the reduced axial stiffness under different tolerance parameters. Additionally, the stiffness reduction factor is incorporated into a refined governing equation of an experimental SCED brace to verify the accuracy of the predicted initial stiffness when the effect of the fabrication tolerances is considered. It is shown that the modified governing equation estimates well the actual initial stiffness. Moreover, this prediction equation can be easily extended to other types of SCED braces once the tolerance parameters have been determined.