The cross-sectional geometry of an embedded microchannel influences the electromechanical response of a soft microfluidic sensor to applied surface pressure. When a pressure is exerted on the surface of the sensor deforming the soft structure, the cross-sectional area of the embedded channel filled with a conductive fluid decreases, increasing the channel's electrical resistance. This electromechanical coupling can be tuned by adding solid microspheres into the channel. In order to determine the influence of microspheres, we use both analytic and computational methods to predict the pressure responses of soft microfluidic sensors with two different channel cross-sections: a square and an equilateral triangular. The analytical models were derived from contact mechanics in which microspheres were regarded as spherical indenters, and finite element analysis (FEA) was used for simulation. For experimental validation, sensor samples with the two different channel cross-sections were prepared and tested. For comparison, the sensor samples were tested both with and without microspheres. All three results from the analytical models, the FEA simulations, and the experiments showed reasonable agreement confirming that the multi-material soft structure significantly improved its pressure response in terms of both linearity and sensitivity. The embedded solid particles enhanced the performance of soft sensors while maintaining their flexible and stretchable mechanical characteristic. We also provide analytical and experimental analyses of hysteresis of microfluidic soft sensors considering a resistive force to the shape recovery of the polymer structure by the embedded viscous fluid.