Facet formation during crystal growth is simulated by using the phase field model in two dimensions. Instead of moderate anisotropy of the often-used form 1 + delta cos 4theta, several functions having strong anisotropy are explored. For simplicity, the interfacial energy is assumed to be isotropic, so only the anisotropy in the kinetic coefficient is considered. This results in the formation of a nearly flat face when the anisotropy function has a narrow minimum at a certain direction, for example 45degrees for four-fold symmetry. Two types of functions are studied in this paper; Type 1: q(1)(theta) = 1 + delta - 2delta(1 - cos4theta)(n)/2(n), and Type 2: q(2)(theta) = 1 -delta + 2deltatanh(k/\tan2theta\). A "facet" is formed at the 45degrees direction for each case. This "facet" is not completely flat for q(1), but a real facet is obtained for q(2). The crystal shapes depend on the parameters delta, n and k in the anisotropy functions. A wider facet is formed for larger delta for both q(1) and q(2), whereas, larger values of n in q(1) and k in q(2) lead to more pronounced facets. Results obtained by using the phase field model are in good agreement with Wulff shapes for the kinetic coefficient. Finally, corner formation is simulated by using similar anisotropy functions with maxima at 45degrees. (C) 2003 Elsevier Science B.V. All rights reserved.