Biocomposites were prepared using epoxidized linseed oil and flax fibre reinforcements in different assemblies. Epoxidized linseed oil was cured by two different anhydrides to check how its thermomechanical properties can be influenced. As reinforcements, nonwoven mat, twill weave and quasi-unidirectional textile fabrics with two different yarn finenesses were used. Their reinforcing effect was determined using dynamic mechanical analysis in flexure. Dynamic mechanical analysis served to determine the glass transition temperature (T_g) also. Shape-memory properties were derived from quasi-unconstrained flexural tests performed near to the T_g of the epoxidized linseed oil and its biocomposites. Flax reinforcement reduced the T_g that was attributed to off-stoichiometry owing to chemical reaction between the hydroxyl groups of flax and anhydride hardener. The shape-memory parameters were moderate or low. They were affected by both textile content and type.