Summary: Least-squares spectral element methods seem very promising since they combine the generality of finite element methods with the accuracy of spectral methods, and also theoretical and computational advantages in the algorithmic design and implementation of least-squares methods. The new element in this work is the choice of spectral elements for the discretization of least-squares formulation for its superior accuracy due to high-order basis-functions. The main issue of this paper is the derivation of a least-squares spectral element formulation for Stokes equations and the study of influence of boundary conditions on coercivity relations. The numerical simulations confirm the usual exponential rate of convergence when \(p\)-refinement is applied, which is typical of spectral element discretization.