Effective and reliable reservoir monitoring is critically important for optimizing oil/gas production and ensuring safe geologic carbon sequestration. It requires an optimal sensor deployment that uses a minimum number of sensors to record the most significant information resulting from reservoir property changes. Conventional monitoring survey designs are typically based on seismic-wavefield illumination analyses, which cannot alone determine the best receiver locations for effective and reliable monitoring of reservoir property changes. We propose a new approach for designing seismic monitoring surveys by analyzing the sensitivities of elastic waves with respect to reservoir geophysical property changes. The method is based on differentiating the elastic-wave equations with respect to geophysical parameters. The resulting sensitivity equations are solved simultaneously with the elastic-wave equations using a finite-difference scheme. Numerical studies confirm that time-lapse seismic survey designs based on elastic-wave sensitivity analysis can be totally different from those based on elastic-wavefield illuminations. For time-lapse seismic monitoring, receivers should be placed at locations where elastic-wave sensitivities are significant. Modeling of elastic-wave sensitivity propagation provides a fundamental tool for effective seismic monitoring survey designs.