A new functional-structural model SUNLAB for the crop sunflower ({\itshape Helianthus annuus} L.) was developed. It is dedicated to simulate the sunflower organogenesis, morphogenesis, biomass accumulation and biomass partitioning to organs. It is adapted to model phenotypic responses of different genotypic variants to diverse environmental factors including temperature stress and water deficit. A sensitivity analysis was conducted to quantify the relative parameter influences on the main trait of interest, the grain yield. The model was calibrated for four genotypes on two experimental datasets collected on plants grown under standard non-limiting conditions and moderate water stress. Its predictive ability was then tested on an additional dataset. The four considered genotypes - ``Albena'', ``Melody'', ``Heliasol'' and ``Prodisol'' - are the products of more than 30 years of breeding effort. Comparing the values found for the four parameter sets associated to each variant, allows to identify genotype-specific parameters. The model also provides a novel way of investigating genotype performances under different environmental conditions. These promising results are a first step towards the potential use of the model as a support tool to design sunflower ideotypes adapted to the current worldwide ecological and economical challenges and to assist the breeding procedure.