A strategy was presented for quantitative analysis of trace elements in a glass sample by laser ablation inductively coupled plasma tandem quadrupole mass spectrometry (LA-ICP-QMS/QMS) with an octapole reaction cell (ORC). Silicon in the glass was used as the internal standard as well as the matrix for making the calibrating solutions. Sample aerosols generated by the laser ablation system were introduced into the dual pass spray chamber through the make-up gas port. Calibrating solutions were nebulized into the spray chamber using a microflow nebulizer. The silicon matrix-matched calibrating solutions produced a calibration curve capable for the quantitative analysis of trace elements in a silicate glass sample, NIST SRM 612. The analytical results agreed with the certified values, taking into consideration their expanded uncertainties. The detection limits for Cr, Mn, Fe, Ni, Cu, As, Sr, Ag, Cd, Sb, Ba, and Pb, were respectively 0.