Optofluidic transport involves the use of electromagnetic energy to transport nanoparticles through the exploitation of scattering, adsorption and gradient (polarization) based forces. This paper presents a new approach to stability analysis for a system of broad applicability to such transport, namely the optical trapping of dielectric particles in the evanescent field of low index (polymer) and high index (silicon) solid-core waveguide structures integrated with microfluidics. Three-dimensional finite element based simulations are used to determine the electromagnetic and hydrodynamic field variables for the system of interest. The net force acting on particles is determined through evaluation of the full Maxwell and flow shear stress tensors, and a trapping stability number is obtained by comparing the work required to remove a particle from the waveguide with available random thermal energy. These forces are correlated to controllable experimental parameters such as particle size, fluid velocity, and channel height, and a series of trapping stability diagrams is produced which detail the conditions under which optofluidic transport is possible.