Samples of PM10 and PM2.5 fractions were collected between the years 2010 and 2013 at the urban area of Krakow, Poland. Numerous types of air pollution sources are present at the site; these include steel and cement industries, traffic, municipal emission sources and biomass burning. Energy dispersive X-ray fluorescence was used to determine the concentrations of the following elements: Cl, K, Ca, Ti, Mn, Fe, Ni, Cu, Zn, Br, Rb, Sr, As and Pb within the collected samples. Defining the elements as indicators, airborne particulate matter (APM) source profiles were prepared by applying principal component analysis (PCA), factor analysis (FA) and multiple linear regression (MLR). Four different factors identifying possible air pollution sources for both PM10 and PM2.5 fractions were attributed to municipal emissions, biomass burning, steel industry, traffic, cement and metal industry, Zn and Pb industry and secondary aerosols. The uncertainty associated with each loading was determined by a statistical simulation method that took into account the individual elemental concentrations and their corresponding uncertainties. It will be possible to identify two or more sources of air particulate matter pollution for a single factor in case it is extremely difficult to separate the sources.