The caustic of a smooth surface in the Euclidean 3-space is the envelope of the normal rays to the surface. It is also the locus of the centres of curvature (the focal points) of the surface. This is why it is also referred to as the focal set of the surface. It has Lagrangian singularities and its generic models are given in [1] (see Figure 2). The aim of this paper is to define the caustic C(M) of a smooth surface M embedded in the Minkowski 3-space and to study its geometry. We denote by the LD the locus of points on M where the metric is degenerate. If M is a closed surface then its LD is not empty. At a point on the LD the “normal” line to M is lightlike and is tangent to M . Also, the focal set of M is not defined at points on the LD. We define the caustic of M as the bifurcation set of the family of distance squared functions on M . Then C(M) coincides with the focal set of M \ LD and provides an extension of the focal set to the LD. We study the local behaviour of the metric on C(M).