  Classical equations of motion for three-dimensional sigma-models in curved
background are solved by a transformation that follows from the Poisson-Lie
T-plurality and transform them into the equations in the flat background.
Transformations of coordinates that make the metric constant are found and used
for solving the flat model. The Poisson-Lie transformation is explicitly
performed by solving the PDE's for auxiliary functions and finding the relevant
transformation of coordinates in the Drinfel'd double. String conditions for
the solutions are preserved by the Poisson-Lie transformations. Therefore we
are able to specify the type of sigma-model solutions that solve also equations
of motion of three dimensional relativistic strings in the curved backgrounds.
Simple examples are given.
