Multiple Correspondence Analysis (MCA) and log-linear modeling are two techniques for multi-way contingency table analysis having different approaches and fields of applications. Log-linear models are interesting when applied to a small number of variables. Multiple Correspondence Analysis is useful in large tables. This efficiency is balanced by the fact that MCA is not able to explicit the relations between more than two variables, as can be done through log-linear modeling. The two approaches are complementary. We present in this paper the distribution of eigenvalues in MCA when the data fit a known log-linear model, then we construct this model by successive applications of MCA. We also propose an empirical procedure, fitting progressively the log-linear model where the fitting criterion is based on eigenvalue diagrams. The procedure is validated on several sets of data used in the literature.