Ion-temperature-gradient (ITG) driven modes in general three-dimensional geometry are investigated using a physical model based on the linearized Braginskii two-fluid equations. The resulting equations are solved globally as an eigenvalue problem without using the ballooning approximation. As a first application of the code developed we calculate the most unstable ITG modes for vacuum field configurations of an ℓ = 2 stellarator and the Wendelstein 7-X (W7-X) stellarator.The Fourier spectra of the modes found do not show a pronounced influence of three-dimensional geometry. The space structure of the solution for the ℓ = 2 stellarator configuration is nearly axisymmetric, while for the W7-X configuration it is more complicated. The properties of the solutions are discussed in connection with the two-fluid model used.