The theory of shear-flow-induced coalescence of monodisperse Newtonian droplets in Newtonian and viscoelastic (described by the Maxwell model) matrices has been derived. Changes in flattening of droplets during coalescence are considered. Calculated dependences on the system parameters of probability, P-c, that the droplet collision is followed by their fusion for Newtonian systems agree qualitatively with the Rother-Davis theory [Phys. Fluids 13, 1178-1190, (2001)]. Values of P-c for a certain set of parameters are substantially affected by the model used to describe mobility of the interface. It has been found that increasing elasticity (relaxation time) of the matrix leads to decreasing P-c irrespective of mobility of the interface. This decrease is small for short relaxation times but pronounced for long relaxation times. The shapes of the dependences of P-c on the droplet radii and the shear rate are similar for systems with a Newtonian matrix but differ qualitatively for systems with a viscoelastic matrix. Results of the theory show that P-c for viscous and viscoelastic matrices can be semiquantitatively approximated by a product of probability for spherical droplets and probability for highly flattened droplets, calculated from Janssen's theory ["Dynamics of liquid-liquid mixing," Ph.D. thesis, Eindhoven University of Technology, Eindhoven, The Netherlands, 1993] for a viscous system. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4739930]