<p>In multi-bolted timber joints, elastic interaction during the tightening process of bolts can cause axial force reduction in previously fastened bolts. While Finite Element Analysis (FEA) can effectively predict this phenomenon, its high computational cost presents a challenge for practical design applications involving numerous parameters. This study proposes a new, high-precision, and computationally efficient mechanical model to evaluate the reduction of bolt axial force. The proposed model improves conventional methods in two primary ways. First, it introduces a new embedment displacement function, expressed in a polar coordinate system, to accurately capture the unique anisotropic embedment behavior of timber. Second, it incorporates the transition mechanism from partial to full compression under the washer, which significantly enhances prediction accuracy, particularly for closely spaced bolts. A method was established to systematically identify the constants required for the proposed model using a single-bolt FEA. The validity of the proposed model was investigated by comparing its predictions with FEA results for 2-bolt and 8-bolt joint configurations, demonstrating excellent agreement with maximum relative errors of 8.4% and 11.1%, respectively. These results confirm that the proposed model can serve as a reliable design tool for predicting residual axial force in complex bolted timber joints and for determining optimal tightening sequences, eliminating the need for case-by-case FEA.</p>