A non-uniform line source has a continuous spatial variation of activity along its length. It may not be possible to divide such a source into smaller sources of uniform activity. Such situation may arise in case of a pipe carrying radioactivity in liquid form. A Mathematica based code was developed for calculating uncolIided flux due to a line source having Gaussian distribution of activity and also a line source with uniform activity placed in air or a non-attenuating medium for comparison. Uncollided flux due to a uniform cylindrical source behind a slab shield was also calculated by replacing it with an equivalent uniform line source using another Mathematica based code and it's output was compared to a point kernel method based code GUI2QAD-3D. Both the codes employ numerical integration.