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Consider the commutative algebra $\mathbb{B}$ over the field of complexnumbers with the bases $\{e_1,e_2\}$ such that %satisfying the conditions$(e_1^2+e_2^2)^2=0$, $e_1^2+e_2^2\ne 0$. %$\mathbb{B}$ is unique.  Let $D$ be a domain in $xOy$, $D_{\zeta}:=\{xe_1+ye_2:(x,y) \in D\}\subset\mathbb{B}$. We say that $\mathbb{B}$-valued function $\Phi \colon D_{\zeta}\longrightarrow \mathbb{B}$, $\Phi(\zeta)=U_{1}\,e_1+U_{2}\,ie_1+U_{3}\,e_2+U_{4}\,ie_2$, $\zeta=xe_1+ye_2$, $U_{k}=U_{k}(x,y)\colonD\longrightarrow \mathbb{R}$, $k=\bar{1,4}$, is {\em monogenic} in $D_{\zeta}$iff $\Phi$ has the classic derivative in every point in $D_{\zeta}$. Every$U_k$, $k=\bar{1,4}$, is a biharmonic function in $D$. A problem on finding anelastic equilibrium for isotropic body $D$ by given boundary values on$\partial D$ of partial derivatives $\frac{\partial u}{\partial v}$,$\frac{\partial v}{\partial y}$ for displacements $u$, $v$ is equivalent to BVPfor monogenic functions, which is to find $\Phi$ by given boundary values of$U_1$ and $U_4$.

$\mathbb{B}$-valued monogenic functions and their applications to boundary value problems in displacements of 2-D Elasticity