Motivated by experimental observations on premixed-gas flame propagation in Hele-Shaw cells, this work analyzes quasi-isobaric flame propagation between two adiabatic parallel plates using a simple quasi-2D formulation based on averaging the flow properties across the cell gap. Instabilities associated with thermal expansion, buoyancy, viscosity change across the front and differential diffusion of thermal energy and reactants are investigated with one-step chemistry, constant heat capacity and variable transport coefficients through time-dependent computations of the flame front evolution in large domains. These instabilities are found to induce flame wrinkling which increases flame surface area and thus propagation speeds in ways different from those associated with freely propagating flames. The simulations are compared with experiments in Hele-Shaw cells: very good qualitative and (in some cases) quantitative agreement is found. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.