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Analytic solutions (ASs) for the spectral responses of waveguide devices with raised-cosine-apodized (RCA) gratings are presented.The waveguide devices include short-and long-period RCA-gratings,RCA-grating-based interferometers as Fabry-Perot,Mach-Zehnder and Michelson interferometers.The calculations based on the analytic solutions are demonstrated and compared with those based on the transfer matrix (TM) method preferred,which has confirmed that the AS-based analysis is with enough accuracy and several thousands times the efficiency of the TM method.