In a low-Mach-number counterflow geometry, steadily propagating twin and triple flames are investigated. A complete numerical model of such flames is presented including a Galilean-like transformation to achieve steadiness of the flames in a moving frame of reference. The model is based on a similarity transformation of the fundamental conservation equations in primitive variables, which transforms the inherently three-dimentional problem to two space dimensions. Suitable boundary conditions are derived employing potential theory. The governing equations are discretized by a finite element method on an unstructured triangulized grid. Employing a local adaptive mesh-refinement procedure, for H-2 - O-2 systems with both a global one-step model and a detailed mechanism of elementary reactions, numerical solutions have been obtained.