  Recent developments of microscopic mechanical experiments allow the
manipulation of individual polymer molecules in two main ways: \textit{uniform}
stretching by external forces and \textit{non-uniform} stretching by external
fields. Many results can be thereby obtained for specific kinds of polymers and
specific geometries. In this work we describe the non-uniform stretching of a
single, non-branched polymer molecule by an external field (e.g. fluid in
uniform motion, or uniform electric field) by a universal physical framework
which leads to general conclusions on different types of polymers. We derive
analytical results both for the freely-jointed chain and the worm-like chain
models based on classical statistical mechanics. Moreover, we provide a Monte
Carlo numerical analysis of the mechanical properties of flexible and
semi-flexible polymers anchored at one end. The simulations confirm the
analytical achievements, and moreover allow to study the situations where the
theory can not provide explicit and useful results. In all cases we evaluate
the average conformation of the polymer and its fluctuation statistics as a
function of the chain length, bending rigidity and field strength.
