  The effect of massive scalar perturbations on neutral black string in de
Rham-Gabadadze-Tolley (dRGT) massive gravity is investigated through the study
of the quasi-normal modes~(QNMs). Due to the similarity between the equation of
motion of the field in the black-string and black-hole background, similar
numerical and analytical techniques can be used to explore the behaviour of the
QNMs. We use the asymptotic iteration method (AIM) and the WKB method to
numerically calculate the QNMs of scalar perturbation in the black string
background with positive cosmological constant. High-momentum behaviour of such
QNMs can be analytically approximated by the first-order WKB method with
excellent accuracy. For near-extremal black string with event horizon very
close to the cosmological horizon, the P\"oschl-Teller technique gives accurate
analytic formula for the QNMs. When massive-gravity-parameter $\gamma$
increases, we found that the scalar modes oscillate with higher frequencies and
decay faster. The QNMs of black string in spacetime with negative cosmological
constant are explored in all range of possible $\gamma$ using the spectral
method. We found the movement of the holographic sound poles to collide and
form diffusive poles as $\gamma$ changes from positive to negative values. We
observe no evidence of instability of neutral black string in both positive and
negative cosmological constant cases.
