The proportional odds model is one of the most commonly used regression models in failure time data analysis and has been discussed by many authors (Appl. Stat. 1983; 32:165–171; J. Am. Stat. Assoc. 1999; 94:125–136; J. Am. Stat. Assoc. 1997; 92:960–967; Biometrics 2000; 56:511–518; J. Am. Stat. Assoc. 2001; 96:1446–1457). It specifies that covariates have multiplicative effects on the odds function and is often used when, for example, the covariate effect diminishes over time. Most of the existing methods for the model are for univariate failure time data. In this paper, we discuss how to fit the proportional odds model to multivariate interval‐censored failure time data. For inference, the maximum likelihood approach is developed and evaluated by simulation studies, which suggest that the method works well for practical situations. The method is applied to a set of bivariate interval‐censored data arising from an AIDS clinical trial.