Copula (dependence) functions, which connect marginal distributions to their joint distributions, are useful for modeling linear and nonlinear relationships in multivariate statistical data in the survival analysis studies. Copula is a multivariate CDF with marginally uniform random variables on [0, 1]. Nowadays, copulas have been applied in statistics, insurance, finance, economics, survival analysis, image processing, and engineering applications. The problem of estimating of joint survival function from incomplete data has been considered by a lot of authors. In the special bivariate case, there are numerous examples of paired data representing the times to death of individuals (married couples or twins), the failure times of components of system and others which subject to random censoring. At present, there are several approaches to estimating of survival functions of vectors of lifetimes. Moreover, the random variables (r.v.-s) of interest (lifetimes) and censoring r.v.-s can be also influenced by other variable, often called prognostic factor or covariate. In medicine, dose a drug and in engineering some environmental conditions (temperature, pressure) are influenced to the observed variables. The basic problem consists in estimation of joint distribution of lifetimes by such censored dependent data with used copula (dependence) functions. The aim of this paper is to examine this problem under a right-random censoring model with covariates.