When measuring the elastic (Young's) modulus of cells using AFM, good attachment of cells to a substrate is paramount. However, many cells cannot be firmly attached to many substrates. A loosely attached cell is more compliant under indenting. It may result in artificially low elastic modulus when analyzed with the elasticity models assuming firm attachment. Here we suggest an AFM-based method/model that can be applied to extract the correct Young's modulus of cells loosely attached to a substrate. The method is verified by using primary breast epithelial cancer cells (MCF-7) at passage 4. At this passage, approximately one-half of cells develop enough adhesion with the substrate to be firmly attached to the substrate. These cells look well spread. The other one-half of cells do not develop sufficient adhesion, and are loosely attached to the substrate. These cells look spherical. When processing the AFM indentation data, a straightforward use of the Hertz model results in a substantial difference of the Young's modulus between these two types of cells. If we use the model presented here, we see no statistical difference between the values of the Young's modulus of both poorly attached (round) and firmly attached (close to flat) cells. In addition, the presented model allows obtaining parameters of the brush surrounding the cells. The cellular brush observed is also statistically identical for both types of cells. The method described here can be applied to study mechanics of many other types of cells loosely attached to substrates, e.g., blood cells, some stem cells, cancerous cells, etc.