This paper aims to detect railway vehicle wheel flats and polygonized wheels using an envelope spectrum analysis. First, a brief explanation of railway vehicle wheel problems is presented, focusing particularly on wheel flats and polygonal wheels. Then, three types of wheel flat profiles and three periodic out-of-roundness (OOR) harmonic order ranges for the polygonal wheels are evaluated in the simulations, along with analyses implemented using only healthy wheels for comparison. Moreover, the simulation implements track irregularity profiles modelled based on the US Federal Railroad Administration (FRA). From the numerical calculations, the dynamic responses of several strain gauges (SGs) and accelerometer sensors located on the rail between sleepers are evaluated. Regarding defective wheels, only the right wheel of the first wheelset is considered as a defective wheel, but the detection methodology works for various damaged wheels located in any position. The results from the application of the methodology show that the envelope spectrum analysis successfully distinguishes a healthy wheel from a defective one.