A gasket for installation in a gap defined by adjacent modular construction units, each having a support frame. The gasket includes at least one layer of structural cement panel; and at least one layer of mineral wool, and the at least one layer of said panel and mineral wool has at least one plate recess configured for accommodating a support plate. A modular building construction is provided, including a plurality of modular units, each unit having a steel frame. Four adjacent units of the plurality form an intersection, and support plates are fastened at upper surfaces of corners formed by each frame. The gasket is disposed in a gap defined at the intersection, the gasket having four plate recesses for accommodating the support plates. In still another embodiment, a method of constructing a building made of modular units including the gasket.