  We study the decomposition problem for tensor powers of $B_2$-fundamental
modules. To solve this problem singular weight technique and injection fan
algorithms are applied. Properties of multiplicity coefficients are formulated
in terms of multiplicity functions. These functions are constructed showing
explicitly the dependence of multiplicity coefficients on the highest weight
coordinates and the tensor power parameter. It is thus possible to study
general properties of multiplicity coefficients for powers of the fundamental
$B_2$- modules.
