In this paper, we discuss stereological estimation of mean particle volume tensors in \(\mathbb{R}^3\) from vertical sections. We consider a particle process of compact particles that can be represented as a stationary marked point process. Under the assumption that the particle distribution is invariant under rotations around a fixed axis, called the vertical axis, we show how the mean particle volume tensors can be estimated consistently (in a probabilistic sense) from observations in vertical sections through a sample of particles. In a simulation study, the new estimator has a superior behaviour compared to an earlier estimator based on observations in several optical planes.