First-principles density-functional calculations of the band structure and wave functions around narrow X-like inclusions in 4H-SiC have been performed. X-like inclusions of various thicknesses, corresponding to two, three, and four stacking faults in neighbouring basal planes, have been investigated. The results for the number of bound states in the inclusion, their energies, and wave functions are well described by a simple one-dimensional quantum-well square potential. The quantum-well property of these inclusions suggests that X-like regions in 4H-SiC are efficient planar traps for conduction band electrons.