Electroosmotic pumping in the microchannels fabricated in polycarbonate (PC), polyethyleneterephthalate (PET) and SU-8 polymer substrates was investigated and species transportation was modeled, in an attempt to show the suitability of low cost polymer materials for the development of disposable microfluidic devices. Microchannels and the fluid reservoirs were fabricated using excimer laser ablation and hot embossing techniques. Typical dimensions of the microchannels were 60μm (width) x 50μm (depth) x 45mm (length). Species transportation in the microchannels under electroosmosis was modeled by finite element method (FEM) with the help of NetFlow module of the CoventorWareTM computational fluid dynamics (CFD) package. In particular, electroosmosis and electrophoresis in a crossed microfluidic channel was modeled to calculate the percentage species mass transportation when the concentration shape of the Gaussian input species plug and the location of the injection point are varied. Change in the concentration shape of the initial species plug while it is electroosmotically transported along the crossed fluidic channel was visualized. Results indicated that Excimer laser ablated PC and PET devices have electroosmotic mobility in the range 2 to 5 x10-4 cm2/V.s, zeta potential 30 to 70 mV and flow rates of the order of 1 to 3 nL/s under an electric field of 200 V/cm. With the electroosmotic mobility value of PC the simulation results show that a crossed fluidic channel is electroosmotically pumping about 91% of the species mass injected along one of its straight channels.