Homogeneous investigations of red giant stars in open clusters contribute to studies of internal evolutionary mixing processes inside stars, which are reflected in abundances of mixing-sensitive chemical elements like carbon, nitrogen, and sodium, while {alpha}- and neutron-capture element abundances are useful in tracing the Galactic chemical evolution. The main aim of this study is a comprehensive chemical analysis of red giant stars in the open cluster IC 4756, including determinations of ^12^C/^13^C and C/N abundance ratios, and comparisons of the results with theoretical models of stellar and Galactic chemical evolution. We used a classical differential model atmosphere method to analyse high-resolution spectra obtained with the FEROS spectrograph on the 2.2m MPG/ESO Telescope. The carbon, nitrogen, and oxygen abundances, ^12^C/^13^C ratios, and neutron-capture element abundances were determined using synthetic spectra, and the main atmospheric parameters and abundances of other chemical elements were determined from equivalent widths of spectral lines.