A new effect, the anomalous resisto-acoustic effect, is theoretically predicted. This effect deals with increase in the velocity of surface acoustic waves due to deposition of a thin conducting film on the piezoelectric substrate. The influence of a thin conducting layer on the propagation of surface acoustic waves in a piezoelectric medium is investigated theoretically. It is generally believed that wave velocity would decrease monotonically with increasing sheet conductance of the layer. Our calculations show, however, that in the case of weakly inhomogeneous surface waves, such as Bleustein–Gulyaev and Love waves, there exists a certain conductance interval in which the wave velocity increases with increasing layer conductance. This anomalous behavior is related to the penetration depth of the wave into the substrate. The anomalous effect is present if the penetration depth exceeds a certain critical value, and absent otherwise. The characteristics of surface acoustic waves in various structures containing layers of finite and/or in finite conductivity have been investigated. It is found that under certain conditions vm, the velocity for a metallized surface, may actually be greater than v0, the velocity for an unmetallized surface. The anomalous resisto-acoustic effect allows one to obtain value of Δv/v, the financial velocity change, that is greater than the normally predicted value of Δv/v=(v0−vm)/v0. For example, for Bleustein–Gulyaev waves propagating in Y-cut, X-propagation potassium niobate, values of Δv/v greater than 0.32 can be obtained, compared to the normally predicted value of 0.26. This has significant advantages in improving the performance of various sensing and signal processing devices.