Concept inventories (CIs) are commonly used in pre-post instruction to study student conceptual change. For consistency in assessment interpretation, a CI's assessment construct is desired to maintain invariance across different test times. In this study, the longitudinal measurement invariance (LMI) analysis under the confirmatory factor analysis framework was used to examine the stability of the factor structure between pretest and post-test of two commonly used CIs, i.e., the Force Concept Inventory (FCI) and Conceptual Survey of Electricity and Magnetism (CSEM). A number of existing and modified models were examined in this paper. The results confirmed that all factor models of the FCI fitted well with both pre- and post-test data. For CSEM, acceptable fits were obtained with a reduced version of the CI. When reliability analysis was performed for the factors of these models, most modified models were found to be more reliable than the existing models. The modified models were further tested in LMI analysis, in which a sequence of models with increasingly restrictive parameter constraints was examined. For the FCI, LMI analysis demonstrated the existence of partial strict invariance, i.e., common factor structures, factor loadings, and item thresholds, and equally observed residual variances for all the items except items 2 and 29. For the CSEM, after excluding 10 items, a reduced version was found to hold the strict invariance criteria. These findings reveal that changes in scores of the whole FCI and the reduced CSEM can be attributed to changes in the latent constructs measured by the CIs, which confirms these two CIs as reliable instruments to study students' conceptual change over time in introductory physics courses.