In this chapter we discuss the flow dynamics of 3D multicellular systems in narrow geometries in response to external mechanical constraints. Quantifying tissue responses to mechanical solicitations is essential for developing theoretical biophysical models to decipher mechanisms controlling morphogenetic events during embryonic growth, or tumor formation and metastasis, during cancer development. Spherical cellular aggregates, made by in vitro aggregation of a few thousands of cells, provide an efficient 3D model system to study tissue mechanics in controlled conditions. We describe pressure-induced aggregate flow into capillary tubes such as micropipettes and microfluidic channels. We demonstrate how the viscoelastic and poroelastic properties of these cellular aggregates are measured, and we describe how mechanical signals can trigger collective active responses from cells, hence modifying the mechanics of the tissue. We close the chapter by discussing applications to developing tissues and other living systems.