A novel numerical framework for conducting linear stability analysis of two-dimensional steady laminar flows is presented. Using two case studies involving analysis of thermal and laminar flows, stability of laminar flows in the numerical sense is addressed. The two-dimensional base flow is computed by using the lattice Boltzmann method for various values of the controlling parameter (Reynolds number for flow past a square cylinder and Rayleigh number for double-glazing problem). Subsequently, the perturbed equations with two-dimensional disturbances are linearized and form a set of partial differential equations that govern the evolution of these perturbations. Using normal mode analysis, the eigenvalues of the resultant equation are used to determine the stablilty of the base flow. © 2018 by the authors of the abstracts.