  The biharmonic equation arises in areas of continuum mechanics including
linear elasticity theory and the Stokes flows, as well as in a radar imaging
problem. We discuss the reflection formulas for the biharmonic functions
$u(x,y)\in\mathbb{R}^2$ subject to different boundary conditions on a
real-analytic curve in the plane. The obtained formulas, generalizing the
celebrated Schwarz symmetry principle for harmonic functions, have different
structures. In particular, in the special case of the boundary, $\Gamma_0
:=\{y=0\}$, reflections are point to point when the given on $\Gamma_0$
conditions are $u=\partial_nu=0$, $u=\Delta u=0$ or $\partial_nu=\partial
n\Delta u=0$, and point to a continuous set when $u=\partial_n\Delta u=0$ or
$\partial_nu=\Delta u=0$ on $\Gamma_0$.
