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Numerous evidence suggests that thick-film resistors are close to a metal– insulator transition and that tunneling processes between metallic grains are the main source of resistance. By theoretical analysis of various percolative resistor network models we show that the piezoresistive response under imposed uniaxial strain is strongly dependent on the concentration of the conducting phase. In particular, the piezoresistive anisotropy is reduced as the system approaches its percolation threshold, following a power law in the critical region. We propose a simple relation between the conductance and the piezoresistive anisotropy valid in the critical region.