In time-lapse (also called 4D) seismic analysis, the time shift of a certain seismic reflection event is caused by changes in the seismic velocity and the depth of the event. An interpretation of 4D time shifts is normally simplified by neglecting displacement changes (strains) or assuming linear relations between thickness and velocity strains. Here, we go beyond these assumptions and propose a least-squares optimization method to simultaneously estimate the thickness and velocity strains in vertical transverse isotropic media from angle-dependent 4D seismic time strains. Through examples from synthetic and field data, we show that 4D thickness strains, velocity strains, and anisotropic parameter changes can be estimated simultaneously without prior knowledge about the geomechanics of the survey area. Our time-strain inversion method can be applied to any other 4D seismic data set in which angle-stack images are available. We see that our method has high potential in many other applications, because thickness and velocity strains are the fundamental components of most physical properties used in 4D seismic and geomechanics applications.