This paper is concerned with the numerical modeling of a slow (creeping) flow using a particle-based simulation technique, known as dissipative particle dynamics (DPD), in which the particles' mass is allowed to approach zero to simultaneously achieve a high sonic speed, a low Reynolds number, and a high Schmidt number. This leads to a system of stiff stochastic differential equations, which are solved efficiently by an exponential time differencing (ETD) scheme. The ETD-DPD method is first tested in viscometric flows, where the particle mass is reduced down to 0.001. The method is then applied for the modeling of rigid spheres in a Newtonian fluid by means of two species of DPD particles, one representing the solvent particles and the other, the suspended particle. Calculations are carried out at particle mass of 0.01, with corresponding Mach number of 0.08, Reynolds number of 0.05, and Schmidt number of 6.0 x 10(3). Stokes results are used to determine the DPD parameters for the solvent-sphere interaction forces. The method obeys equipartition and yields smooth flows around the sphere with quite uniform far-field velocities. (C) 2013 The Society of Rheology. [http://dx.doi.org/10.1122/1.4789444]