  Starting from the static Fukuyama-Lee-Rice equation for a three-dimensional
incommensurate charge density wave (CDW) in quasi one-dimensional conductors a
solvable model for local phase pinning by impurities is defined and studied. We
find that average CDW energy and average pinning force show critical behaviour
with respect to the pinning parameter $h$. Specifically the pinning force
exhibits a threshold at $h=1$ with exponent $\beta=2$. Our model examplifies a
general concept of local impurity pinning in which the force exerted by the
impurity on the periodic CDW structure becomes multivalued and metastable
states appear beyond a threshold. It is found that local impurity pinning
becomes less effective at low temperatures and may eventually cease completely.
These results are independent of spatial dimensionality as expected for local
impurity pinning. Comparison with Larkin's model is also made.
