Described are methods for monitoring of stresses and other material properties. These methods use measurements of effective electrical properties, such as magnetic permeability and electrical conductivity, to infer the state of the test material, such as the stress, temperature, or overload condition. The sensors, which can be single element sensors or sensor arrays, can be used to periodically inspect selected locations, mounted to the test material, or scanned over the test material to generate two-dimensional images of the material properties. Magnetic field or eddy current based inductive and giant magnetoresistive sensors may be used on magnetizable and/or conducting materials, while capacitive sensors can be used for dielectric materials. Methods are also described for the use of state-sensitive layers to determine the state of materials of interest. These methods allow the weight of articles, such as aircraft, to be determined.