To understand the relation between the resonant period drop of the torsional oscillator (TO) containing the solid helium and its elastic modulus change, we simultaneously measure both phenomena using a TO by inserting concentric piezoelectric (PZT) transducer. Even we observe the similarities of the temperature, 3He concentration and frequency, remarkable discrepancy in the amplitude responses are observed. To investigate this result, we construct the perpendicularly stacked PZT transducers to measure the shear modulus in parallel to and perpendicular to the driving displacement direction. We find that our samples are composed of a few of highly oriented gains or a sufficiently small number of domains connected with a certain preferential orientation. Therefore, the discrepancies in the drive dependence of simultaneous measurement is originated from a change of an elastic property of solid helium.