**MSC:**- 35J25 Boundary value problems for second-order, elliptic equations
- 35J55 Boundary value problems for elliptic systems
- 35C15 Integral representations of solutions of PDE
- 35Q72 Other equations from mechanics

for general second order elliptic equations and systems in a polyhedral cone.

We obtain point estimates of Green's matrix in different areas of the cone. The proof of

these estimates is essentially based on weighted $L_2$ estimates for weak solutions and

their derivatives.

As examples, we consider the Neumann problem to the Laplace equation and the Lam\'e system.