Critical elements are essential in a variety of high-tech applications. In the context of the circular economy, demand has arisen for technologies that are able to recover high-tech metals from wastes and byproducts. The aim of the present study is to investigate the leaching potential of critical elements from coal fly ash (CFA) using carboxylic acids as a milder yet efficient leaching agent. The leaching efficiency of citric acid and acetic acid was investigated in a simple single step process (pH 2.5-3.5 depending on the fly ash used) and the effect of acid type, acid concentration, temperature, and time on the process was studied with leaching experiments and the parameters were simulated using a non-linear equation and the uniform random distribution through MONTE CARLO simulations. Two coal fly ashes were studied. The major constituents of the fly ashes were analyzed by X-ray fluorescence spectroscopy (XRF) and their mineralogy was studied by X-ray powder diffraction (XRD). The content of fly ash samples in critical elements (Zn, Cr, Co, Mn, Ni, La, Ce, Li) as well as critical elements in the leachates, was determined by ICP–MS. The results revealed that citric acid appeared to be a better leaching agent, in most cases, with leaching efficiencies that reached 88%. The leaching efficiency for both acids in all cases was much higher for transition metals studied, compared to La, Ce, and Li. Experimental results adequately fitted to a non-linear equation in all cases with MARE < 11% and equations relating elements’ recovery to the three parameters investigated were successfully (MARE<16%) produced.