Elastic interactions between defects are investigated in thin layers. Unlik
e the classical repulsive law 1/r(3) (r = defect separation), we discover t
hat defects in thin layers may either attract or repel each other depending
on the direction (though elastic deformation is isotropic) with respect to
the local geometric force distribution caused by the defect. Moreover, the
force distribution fixes the exponent in the power law 1/r(n) (e.g., in a
square lattice n = 4). We discuss the implication of this new behavior in v
arious situations.