A procedure is presented for determining the three-dimensional elastic
ity solutions for free vibration analysis of simply supported thick sk
ew plates, The exact expressions of strain and kinetic energies are de
rived from linear, small-strain, three-dimensional elasticity theory.
To allow the treatment of soft and hard simple support conditions, set
s of three-dimensional spatial displacement functions are expressed in
terms of unit normals to the edges. By virtue of the three-dimensiona
l elasticity theory, the present method does not require a special tre
atment for stress singularity at the obtuse corners. This method is al
so demonstrated to be free from shear locking phenomena. The significa
nt difference in the vibration response of skew plates with soft and h
ard simple support conditions is highlighted, The influence of skew an
gle an the eigenvalues of thick skew plate is discussed in the context
of the three-dimensional elasticity solutions.