Although yield stress fluids are very present today in everyday life and in industry, their flow behavior is still poorly understood and the databases are incomplete at this time. The present experimental and numerical study focuses on laminar nonrecirculating flows of an elastoviscoplastic model fluid in a rectangular duct. An original experimental set-up has been developed. The Particle Image Velocimetry method is used for analyzing the kinematical fields. Results provided concern the morphology of the flow and the evolution of the velocity field around a cylindrical obstacle. Information is provided on the size of the rigid zones where the fluid behaves as a solid. The experimental data are compared with numerical results involving a regularized Herschel-Bulkley viscoplastic model. (c) 2016 American Institute of Chemical Engineers AIChE J, 62: 4554-4563, 2016