Wood is a noble, versatile, and renewable material which plays an important role in sustainable manufacturing. The present study shows that it is feasible to laser bend veneers of different wood species by applying infrared energy in the form of a scanned laser beam. Bending height, i.e., deflection of the veneer measured as the vertical elevation of its edge points from the horizontal plane; were achieved on three wood types, namely: beech, yesquero, and ulmo. Process parameters and wood properties considered relevant to the response variable are laser energy, moisture content, water loss, density, and wood species. Experimental results indicate that specimens 15 cm long, 3.5 cm wide and 1.5 mm thick achieved bending heights ranging from 0.35 cm (beech) up to 4.8 cm (yesquero). Largest average height of 4.45 cm was achieved in beech veneers at equilibrium moisture content of 13% under maximum laser energy of 1061 J. On the other hand, ulmo specimens having 0% moisture content, after oven drying for 72 hour at 40ºC, also showed considerable average deflection height of up to 3.1 cm. This reaffirms that free water loss is not the only mechanism for fibre contraction, but that cell wall bound water loss during the laser wood interaction also causes considerable shrinkage, as expected. Machine-Learning analysis of the experimental data suggests the algorithm that better suited the response variable was the Gaussian Process regression since it showed the highest correlation coefficient and the lower RMSE. Confirming that moisture content explains almost 45% of the model's predictability, followed by laser energy with 35%, while water loss (both free and bound) was ranked third.