Rare earth elements (REEs) are examined from Standard reference materials in a liquid state (after digestion with acids) utilizing ICP-MS and in a solid form after fusion with lithium tetra borate to have transparent fused targets utilizing LA-ICP-MS. NIST 612 and NIST 614 serve as the external standards for the Laser ablation unit merged with the ICP-MS (LA-ICP-MS). This paper aims to investigate the key differences between the two approaches to data analysis. The precision of the measurements is discussed for each element that was measured. When measured by LA-ICP-MS, the relative standard deviation is typically middle 1 to 8 percent, while when measured by ICP-MS, it ranges from 1 to 3 percent. The measurements' accuracy was reported and are found, within ± 10% by LA-ICP-MS and ± 5% by ICP-MS. Techniques like the inductively coupled plasma mass spectrometer and the laser ablation that may be added to it are valuable tools for precisely measuring rare earth elements (REEs).