Rayleigh-Bénard convection is investigated in rotating annular cavities at a moderate rotationrate (square root of the Taylor number) Omega= 60. The onset of convection is in the form of azimuthaltraveling waves that set in at the sidewalls and at values of the Rayleigh number significantly belowthe value of the onset of convection in an infinitely extended layer. When curvature effect becomessignificant, the waves traveling along the sidewalls have different critical Rayleigh numbers and com-plex Guinzburg-Landau equations are no longer applicable. The present study addresses the effectsof curvature and confinement on the onset of sidewall convection by using three-dimensional spectralsolutions of the Oberbeck-Boussinesq equations. Such solutions demonstrate that the curvature ofthe outer boundary promotes the onset of the wall mode, while the opposite curvature of the innerboundary tends to delay the onset of the wall mode. When radial confinement is increased the twoindependent traveling waves can interact and eventually merge to form a nearly steady pattern ofconvection.