Rheometric data for suspensions of bubbles and/or particles in a Newtonian suspending liquid. Experimental suspensions are intended as analogues for multiphase magma and lava (containing volatile bubbles and solid crystals). The dataset comprises data collected using a Anton Paar MCR702 rheometer. A Newtonian working fluid (sugar syrup) suspends variable fraction of gas bubbles and solid particles. Data relating to suspensions of bubbles only are found in the folder Bubble_Suspensions, and data relating to suspensions of bubbles and particles are found in the folder 3Phase_Suspensions. For all suspensions, rheometric data were collected in a wide-gap concentric cylinder geometry using both rotational rheometry (flow curves) and oscillatory rheometry (frequency sweeps). Bubble fraction and particle fraction are varied systematically. In each folder a matlab script is provided which facilitates extraction and analysis of the raw data, which are held in .csv files