In this paper, we present the numerical simulation results of deformation and breakup of a multi-core compound droplet. The method used is a two-dimensional front-tracking method with a modification for multi-layer droplets. The droplet is placed at the center of the domain whose top and bottom boundaries move in the opposite directions to create the shear flow. We vary the values of various parameters in specific ranges to investigate their effects on the deformation and breakup of the multi-core compound droplet in shear flow. We mainly focus on the two-core compound droplets. Basing on the numerical results, we reveal various patterns (i.e. modes) of deformation and breakup: non-breakup types 1 and 2, breakup types 1, 2, 3 and 4. For the first non-breakup type (type 1), the outer interface is deformed with two inner droplets accumulating at the center whereas in the other non-breakup type (type 2), the inner droplets move to the two furthest ends. The non-breakup type 1 generally changes to the breakup type 4, at some critical parameters, in which the compound droplet breaks up into simple droplets at its ends with a smaller daughter compound droplet in between. The non-breakup type 2 transits to the breakup type 1 or type 2, depending on the flow conditions, with the formation of two smaller daughter compound droplets at the ends. The remaining breakup mode (type 3) is a mixed breakup mode that is a combination of the breakup types 2 and 4. These deformation and breakup patterns are mapped onto a Re-Ca diagram. We also propose some other diagrams based on the variations of the inner droplet location. In addition, we investigate the effect of the number of the inner droplets encapsulated in the compound droplet on its deformation and breakup. (C) 2018 Elsevier Ltd. All rights reserved.