Objective. This study aimed to produce a three-dimensional liver elasticity map using the finite element method (FEM) and respiration-induced motion captured by T1-weighted magnetic resonance images (FEM-E-map) and to evaluate whether FEM-E-maps can be an imaging biomarker comparable to magnetic resonance elastography (MRE) for assessing the distribution and severity of liver fibrosis. Approach. We enrolled 14 patients who underwent MRI and MRE. T1-weighted MR images were acquired during shallow inspiration and expiration breath-holding, and the displacement vector field (DVF) between two images was calculated using deformable image registration. FEM-E-maps were constructed using FEM and DVF. First, three Poisson’s ratio settings (0.45, 0.49, and 0.499995) were validated and optimized to minimize the difference in liver elasticity between the FEM-E-map and MRE. Then, the whole and regional liver elasticity values estimated using FEM-E-maps were compared with those obtained from MRE using Pearson’s correlation coefficients. Spearman rank correlations and chi-square histograms were used to compare the voxel-level elasticity distribution. Main results. The optimal Poisson’s ratio was 0.49. Whole liver elasticity estimated using FEM-E-maps was strongly correlated with that measured using MRE (r = 0.96). For regional liver elasticity, the correlation was 0.84 for the right lobe and 0.82 for the left lobe. Spearman analysis revealed a moderate correlation for the voxel-level elasticity distribution between FEM-E-maps and MRE (0.61 ± 0.10). The small chi-square distances between the two histograms (0.11 ± 0.07) indicated good agreement. Significance. FEM-E-maps represent a potential imaging biomarker for visualizing the distribution of liver fibrosis using only T1-weighted images obtained with a common MR scanner, without any additional examination or special elastography equipment. However, additional studies including comparisons with biopsy findings are required to verify the reliability of this method for clinical application.