It is a well-known fact that laser-induced breakdown spectroscopy (LIBS) has emerged as one of the best analytical techniques for multi-elemental compositional analysis of samples. We report assembling and optimization of LIBS set up using high resolution and broad-range echelle spectrograph coupled to an intensified charge coupled device (ICCD) to detect and quantify trace elements in environmental and clinical samples. Effects of variations of experimental parameters on spectroscopy signals of copper and brass are reported. Preliminary results of some plasma diagnostic calculations using recorded time-resolved optical emission signals are also reported for brass samples.