Focal mechanisms of earthquakes with magnitudes 4.0 and less recorded by a sparse seismic network are usually poorly constrained due to the lack of an appropriate method applicable to finding these parameters with a sparse set of observations. We present a new method that can accurately determine focal mechanisms of earthquakes with (3.70–3.04) using data from a few regional seismic stations. We filter the observed seismograms as well as synthetic seismograms through a frequency band of 1.5–2.5 Hz, which has a good signal‐to‐noise ratio for small earthquakes of the magnitudes with which we are working. The waveforms are processed to their envelopes to make the waveforms relatively simple for modeling. To find the optimal focal mechanism for an event, a nonlinear moment tensor inversion in addition to a coarse grid search over the possible dip, rake, and strike angles at a fixed value of focal depth and a fixed value of scalar moment is performed. We tested the method on 18 aftershocks of (3.70–2.60) of the 2011 5.7 Mineral, Virginia, earthquake and on five aftershocks of (3.62–2.63) of the 2013 4.5 Ladysmith, Quebec, earthquake. Our method obtains accurate focal mechanisms for 16 out of the 21 events that have previously reported focal mechanisms. Tests of our method for different crustal models show that event focal mechanism determinations vary with an average Kagan angle of 30° with the different crustal models. This means that the event focal mechanism determinations are only somewhat sensitive to the uncertainties in the crustal models tested. This study confirms that our method of modeling envelopes of seismic waveforms can be used to extract accurate focal mechanisms of earthquakes with short‐time functions () using at least three regional seismic network stations at epicentral distances of 60–350 km.