  We give an algorithm for finding conformal mappings onto the upper half-plane
and conformal modules of some types of polygons. The polygons are obtained by
stretching along the real axis polyominoes i.e., polygons which are connected
unions of unit squares with vertices from the integer lattice. We consider the
polyominoes of two types, so-called the $P$-pentomino and the $L$-tetromino.
The proofs are based on the Riemann-Schwarz reflection principle and
uniformization of compact simply-connected Riemann surfaces by rational
functions.
