Summaries of typical survival times are often reported in terms of medians. Thus, median regression models, with the median expressed as a (non)linear function of covariates, are appropriate regression models for survival data. For interval censored survival data, the approaches for estimating medians for uncensored and right censored data are not appropriate. The problem becomes more complex when there is clustering in the data and the observations cannot be considered independent. Our goal is to estimate the median regression model for interval censored survival time when the data is clustered due to the presence of unobserved random cluster effects.