Aims.We investigate the influence of longitudinal structuring of the surrounding corona on the modes of oscillation of a coronal magnetic flux tube. Methods: .A partial differential equation is derived for the total pressure perturbation of the fast modes and it is solved analytically in terms of Bessel functions, obtaining a dispersion relation. Results: .The introduction of coronal structuring changes the cutoff frequency, enhancing coronal leakage, so even the fundamental kink mode may become leaky. Structure also modifies the loop's oscillatory frequencies and may result in higher harmonics being trapped. Conclusions: .Depending on the structuring, two competing effects take place: environmental structuring enhances leakage, while loop structuring helps confine the modes. This has important consequences for coronal seismology, leading to the absence of trapped modes for certain parameters and shifts in frequencies.