We report theoretical differential elastic cross sections for scattering of electrons by CF₃ radical (trifluoromethyl or carbon trifluoride) and CF₃H (fluoroform). The calculations were performed with the Schwinger multichannel method at the static-exchange level. Our results for CF₃ are the first cross sections for open-shell molecules with nonlinear geometry. There is no experimental data for e^--CF₃ scattering but the theoretical data for CF₃H are in good agreement with recent experimental results of Tanaka. Our results show interesting similarities between elastic cross sections of e^--CF₃ and e^--CF₃H scattering.