We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles. The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space. We analyze the singular behavior of the integrals (single-layer and double-layer integrals) appearing in the equations. The interfaces are formulated in the tangent angle and arc-length coordinates and, to reduce the stiffness of the evolution equation, the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces. Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.