As a method to shorten the test time of the Force Concept Inventory (FCI), Computerized Adaptive Testing (CAT) is suggested. CAT is a test administered on a computer, where items (i.e. questions) are selected based on the responses of examinees to prior items. As a step of the development, we conducted analyses to find an optimal way for the administration of CAT with the FCI. Specifically, since CAT is based on Item Response Theory (IRT), we examined which IRT model is the most preferable. Using 2812 responses of the FCI of Japanese students, we estimated the item parameters of the One-, Two-, Three-, and Four-parameter logistic model of IRT and then we evaluated the statistics for the goodness of fit and for model selection. Based on the analysis, we suggest that the Two-parameter logistic model is the most preferable for the administration of CAT with the FCI.