The thickness/twist vibrations of a truncated, linearly tapered, quartz‐crystal strip are investigated. The frequency equation is expressed in terms of Bessel functions, with the order, in general, a large irrational number. Frequencies and mode shapes depend on two geometric parameters expressing the taper and a length/thickness ratio. Numerical values for several modes and a range of the geometric parameters are given forAT‐cut quartz to illustrate typical results. Frequencies are only slightly higher than for a corresponding uniform strip, and depend mainly on the maximum thickness of the tapered strip. Motion of the strip is concentrated at the thick end, even for very slight taper, but spreads gradually across the strip as the taper is reduced, approaching in the limit the response of a uniform strip.