Today's standard fabrication processes are just capable of manufacturing slab of photonic and phononic crystals, so an efficient method for analysis of these crystals is indispensable. Plane wave expansion (PWE) as a widely used method in studying photonic and phononic (phoxonic) crystals in full three dimensions is not suitable for slab analysis in its standard form, because of convergence and stability issues. Here, we propose a modification to this method which overcomes these limitations. This improved method can be utilized for calculation of both photonic and phononicmodes in phoxonic slabs. While in the standard threedimensional PWE, Fourier series are used to estimate the field dependence across the normal component of the slab, we expand the fields across the third dimension using eigenmodes of a plain unstructured slab. Despite its approximate nature, this approach is observed to be both much faster and more accurate than the conventional PWEmethod and can give a very accurate estimation of confined propagating modes. As an application example of the proposed method, we investigate a nonreciprocal photonic device. This device is a phoxonic slab waveguide, which changes modes of optical waves by elastic waves and can be used as an optical insulator or mode converter.