The present work is dealing with the transmission ofoblique plane waves through a periodic row of thick-walledchannels of finite length. It is aimed at investigating howsound is transmitted in some parts of the ventilation ductsintegrated in electrical machines used in railways applica-tions.A two-dimensional analytical mode-matching methodwithout flow is proposed, according to which modal ex-pressions are written in sub-domains and matched accord-ing to conservation laws of fluid dynamics. The trans-mission and reflection coefficients are computed from thematching equations. Effects of channel length, frequency,wall thickness, are discussed. A particular attention is paidto the resonances in the system.