In many extra-dimensional models, brane-localized mass terms are introduced in order to decouple unnecessary exotic particles from the four-dimensional effective theory. However, it should be noted that the impacts of the brane-localized terms become smaller as the codimensions increase. Thus it should numerically be checked how heavy the exotic parcticles can be by them. Here we study the effects of a brane-localized mass on
the KK mass eigenvalues and the mode functions of a bulk field in two-dimensional compact space.