Cylindrical acoustic waveguides are considered, the straight one Ω = ℝ × ω ⊂ ℝd and a curved one Ωε. Both have equal constant cross-section ω which is assumed to be symmetric for ε = 1 and asymmetric for a small ε ⊂ (0,1). In the case d > 2 it is proved that under certain restrictions on shape of the cross-section, a local distortion of the cylinder axis which is arbitrary for ε = 1 but small, that is, described by the parameter ε ≪ 1, supports a trapped mode. In other words, the spectral Neumann problem for the Laplace operator in the domain Ωε gets a solution of the exponential decay, i.e., an eigenfunction from the Sobolev space H 1(Ωε). The corresponding eigenvalue λε is embedded into the continuous spectrum and, therefore, possesses a natural instability while its appearance is a result of either a special choice of the axis curvature, or creating an artificial positive cutoff value of the continuous spectrum under the symmetry assumption.