We present a method for numerical computation of conformal mappings from simply or
doubly connected domains onto so-called canonical domains, which in our case are
rectangles or annuli. The method is based on conjugate harmonic functions and properties
of quadrilaterals. Several numerical examples are given.

Let Q be a quadrilateral. Let the function f= u+ iv be a one-to-one conformal mapping of the
domain Ω onto a rectangle Rh={z∈ C: 0< Rez< 1, 0< Imz< h} such that the image of z1, z2,
z3, z4 are 1+ ih, ih, 0, 1, respectively. Then the number h is called the (conformal) modulus
of the quadrilateral Q and we will denote it by M (Q).