During the last decades, the rheology of cells has been studied almost entirely in single cells. While cell-to-cell variation is typically very large and most studies were carried out in the nonlinear viscoelastic regime, we quantify average linear viscoelastic cell properties like storage and loss moduli and normal stress in monolayers of different cell types showing that murine 3T6 fibroblasts, human fibroblasts, and HeLa cells differ considerably in their storage modulus. To this end, we modified a commercial rheometer to set up a parallel-disk configuration at gap widths of a few micrometers and optically detected the cell concentration in the gap. This enables studying the linear viscoelastic behavior of the cells and permits quantifying the impact of drugs affecting the cytoskeleton or the extracellular matrix connection. Thus, due to its high-content approach, without the need of treating the samples in the rheometer, this envisions the use of this method as a fast diagnostic tool. The method also allows for quantitatively studying of the impact of pre-stress on the storage and loss moduli of the cells.