Core mode cutoff is a useful concept not only for a tapered single-core fiber (SCF) but also for a tapered multicore fiber (MCF) to realize cladding mode transmission. In this paper, cut-off conditions of either core mode for tapered SCFs or supermodes for MCFs are theoretically investigated. Rigorous analytical formulas are derived for the modes of SCF by a three-layer waveguide model, and an approximation formula of the cut-off condition is given for the LP01 mode. The supermodes of MCFs are analyzed by the coupling mode theory, and the cut-off condition is calculated by a numerical method. Simulation results show that the in-phase supermode of MCFs has a similar cut-off condition with that of SCF. Based on this property, a convenient approximate formula is given to estimate the cut-off condition of the in-phase supermode for tapered MCFs.