An approximation technique previously developed for straight elastic surface wave guides utilizing thin films is extended and applied to curved guides with large radius‐to‐guide‐width ratios. The dispersion curves for the circular guides are obtained by employing approximate bound modes in place of the actual wave functions, which are not fully bound. This procedure is quite accurate for the determination of dispersion curves in the propagation range of interest. Nevertheless, since the actual wave functions are not fully bound, some radiation is always present in a curved guide. This radiation loss accompanying the approximate bound modes is evaluated. A critical radius‐to‐guide‐width ratio, beyond which a calculation cannot be performed by the method employed, is defined, and it is shown that the radiation attenuation becomes prohibitively large even before this limiting ratio is reached. The problem of the lowest symmetric guided elastic surface wave in a straight guide incident on a curved guide in the shape of a quarter‐circle is treated and the transmitted and reflected waves are determined, including in the calculation only the two lowest modes in each region and the radiation attenuation associated with each mode.