Combined interaction of all the genes forms a central part of the functional system of a cell. Thus, especially the data-based modeling of the gene expression network is currently one of the main challenges in the field of systems biology. However, the problem is an extremely high-dimensional and complex one, so that normal identification methods are usually not applicable specially if aiming at dynamic models. We propose in this paper a subspace identification approach, which is well suited for high-dimensional system modeling and the presented modified version can also handle the underdetermined case with less data samples than variables (genes). The algorithm is applied to two public stress-response data sets collected from yeast Saccharomyces cerevisiae. The obtained dynamic state space model is tested by comparing the simulation results with the measured data. It is shown that the identified model can relatively well describe the dynamics of the general stress-related changes in the expression of the complete yeast genome. However, it seems inevitable that more precise modeling of the dynamics of the whole genome would require experiments especially designed for systemic modeling.