Different kinds of parasitic effects in a nanoprobe are investigated. In this paper we consider the focusing system of nanoprobe, which consists of quadrupole lenses, but some results are also discussed for solenoids as focusing elements. The results of the similar analysis make it possible to design a number of goal-seeking strategies for selecting the optimal beam line structure. The influence of different linear and nonlinear aberrations is investigated using analytical and numerical methods and tools. For this purpose we present the beam line propagator based on a matrix formalism for Lie algebraic tools. In conclusion, some results of fulfilled modeling are analyzed.