The definition of softness and local softness using the density of states (DOS) and local density of states (LDOS) given by Yang and Parr for metals has been casted into working equations and applied to sequences of finite cylindrical fullerenes modeling the (5,5) and (10,10) single-walled capped carbon nanotubes. The behavior of DOS, LDOS, and global and local softness as functions of length and tube type is investigated in the simplest Huckel approximation. DOS-based calculation of global softness gives results that depend less on the details of the electronic structure than those based on the finite-difference approximation. Armchair single-walled nanotubes with larger diameters are softer than those with smaller diameters at the same tube length. Local softness, after fluctuations in the end-cap region, settles down within the first 20 layers of hexagons of the tube body to a constant (diameter-dependent) value.