In many cases it may be beneficial to measure the overall textural properties of an object by a single number rather than focusing on particular parameters in a rheological model. Intuitively, the concept of “firmness” may serve this purpose. Firmness may be used to classify fruits and vegetables by maturity, foods by textural properties, foamed plastics by their cushioning properties, etc. The definition of firmness has hitherto not been rigorously given. Using a previously developed general rheological model, which is suitable for quantifying the behavior of solids made of linear and nonlinear viscoelastic materials, theoretical and experimental groundwork is laid, whereby an object may be subjected nondestructively to a series of minute deformations by vibration excitation, in conjunction with computerized determination of various indexes for automatic classification by firmness. Development of several alternative firmness indexes is described and their relative utility for automatically classifying viscoelastic bodies, such as fruits and vegetables by firmness, is analyzed and compared. A review of model firmness indexes, by which only two‐way classifications are possible, is followed by the introduction of monotonic firmness indexes, where resonance modes are effectively eliminated, when classification into any number of firmness grades with superior sensitivity is possible. The validity and generality of the approach is demonstrated by firmness classification tests on tomatoes and oranges.