  Incommensurate magnetism in CrB$_2$ is studied in terms of a spin model based
on density functional theory calculations. Heisenberg exchange interactions
derived from the paramagnetic phase using the disordered local moment theory
show significant differences compared with those resulting from the treatment
of the material as a ferromagnet; of these two methods, the disordered local
moment theory is found to give a significantly more realistic description. We
calculate strongly ferromagnetic interactions between Cr planes but largely
frustrated interactions within Cr planes. Although we find that the ground
state ordering vector is sensitive to exchange interactions over a large number
of neighbour shells, the $q$-vector of the incommensurate spin spiral state is
satisfactorily reproduced by the theory ($0.213$ compared with the known
ordering vector $0.285\times (2\pi)/(a/2)$ along $\Gamma-{\rm K}$). The strong
geometric frustration of the exchange interactions
  causes a rather low N\'eel temperature (about 97 K), also in good agreement
with experiment.
