Long memory in asset returns and volatilities is a new research area, both in theoretical and empirical modeling of high frequent financial time series. The most popular techniques of time series modeling with long memory is the ARFIMA-FIGARCH, but this fractionality in the integration of time series modeling has not been extended to the Multivariate GARCH models yet. The present paper aims to extend the BEKK’s MGARCH models to take into account the presence of long memory in daily financial time series. Although the proposed procedure is highly non-linear in the fractionality parameters with a serious computational burden, it estimates all the parameters of mean and variance equations in a nonlinear framework and finds a unique solution, by numerical optimization procedures.  In the empirical part of the paper a multivariate FIGARCH is used to check the transmission of volatility  among the automobile industry, machinery leasing and equipment indices in the Tehran Stock Exchange. The results confirm the existence of short memory in both conditional means and conditional variances, and moreover the magnitude of estimated d parameter is remarkably different from those of resulted from GPH and single ARFIMA-FIGARCH. Empirical findings of the MFIGARCH specification were compared with those of BEKK, and the comparison shows that MFIGARCH estimations are consistent with theoretical considerations. Moreover, our findings  confirm the presence of lead and lag effects and information flow between the returns and volatilities of automobile industries and machinery leasing stock prices, and a multilateral information transmission from machinery leasing’s stock towards the Auto industry and machinery parts manufacturing share prices is observed.