The strip shape inheritance model is widely applied to improve the strip shape quality in tandem cold rolling (TCR). However, the inheritance mechanism is still currently unclear. To bridge this gap, this paper presents a new numerical method for calculating the strip crown inheritance factor. In addition, the effects of the entry strip crown on exit strip crown and flatness were quantitatively analysed at each stand in the TCR using a novel three-dimensional (3D) multi-stand elastic–plastic finite element (FE) model. The results show that the strip crown inheritance factor increases slowly from S1 (stand 1) to S3 (stand 3), while rising sharply from S3 to S5 (stand 5), reaching a peak value of 0.495 μm/μm at S5. This trend coincides with that of strip plastic rigidity, which verifies that the strip crown inheritance factor is dependent on the strip plastic rigidity. Furthermore, the variation of strip crown and flatness under different entry strip crowns from S1 to S5 is jointly influenced by the pass reduction and strip plastic rigidity. Moreover, the strip crown inheritance factor increases with the deformation resistance of the strip at both S1 and S5. These findings not only offer a fresh perspective to understand the mechanism of strip crown inheritance, but also provide an important basis for optimising the strip shape control in the TCR process.