Intricate webs of interlinked critical infrastructures such as electrical grid, telecommunication, and transportation are essential for the minimal functioning of contemporary societies and economies. Advances in Information and Communication Technology (ICT) underpin the increasing interconnectivity of these systems which created new vulnerabilities that can be seriously affected by hardware failure, link cut, human error, natural disaster, physical-attacks and cyber-attacks. Failure of a fraction on nodes may lead to failure of dependent nodes in the other networks. Therefore, the main objective of this paper is to investigate the cascades phenomena caused by load shedding between two interconnected networks using Bak-Tang-Wiesenfeld sandpile modeling. We have found that, large avalanche occurred when node degree and/interconnectivity link become dense. In addition, the coupled random-regular networks have been found to be more robust than the coupled Erdos-Renyi networks. However, coupled random-regular networks are vulnerable to random attack and coupled Erdos-Renyi networks are vulnerable to target attack due to the degree distribution.