A method is developed to determine the response of digital seismographs from transient calibration pulses. Based on linear system theory, the digital seismograph is represented by a set of first- and higher-order linear filters characterized by their cutoff frequencies and damping coefficients. The transient calibration pulse is parameterized by a set of instrument constants, and the problem is linearized for small perturbations of the constants with respect to their nominal values. The observed calibration pulse shape is matched in the time domain using an iterative linearized inverse technique. The method is used to derive complete instrument responses for digital seismographs operating at the Borovoye Observatory (BRVK) in Kazakhstan, for which previously only the amplitude responses have been determined. To test this method, we apply it to calibration pulses from a modern digital seismograph system at Kislovodsk (KIV) in northern Caucasus, Russia, and obtain good agreement between known and derived instrument constants. The results of the calibration pulse shape inversion for these seismographs indicate that the method is efficient and that the results are reliable even when microseismic noise is present in the recorded transient calibration pulse. The derived parameters make possible improved quantitative waveform analysis of digital seismograms recorded at BRVK.