  In this work the gravitational Kaluza-Klein (KK) modes are analysed on
string-like braneworlds in six dimensions, namely the thin string-like
Gherghetta-Shaposhnikov (GS) and the thick string-cigar model. We find a new
massless mode in both modes satisfying the respective Schroedinger equation. By
means of numerical analysis for both models, a complete graviton spectrum and
eigenfunctions is attained. Besides the linear regime, the KK spectrum exhibits
a decreasing behavior with an asymmetric mass gap with respect to the massless
mode. The discontinuity is bigger in the GS model, and it is invariant upon the
geometrical flow. A massive mode is obtained in the GS model with a tiny mass
which does not match in any regime. It turns out that in the string-cigar
model, the core brane structure smoothes and amplifies the KK modes near the
brane. Further, the presence of a potential well allows the existence of
resonant massive gravitons for small masses in the string-cigar scenario.
