We present three-dimensional numerical models of convection within the partially molten mantle beneath the ridge axis. The modeling takes into account the cavity flow driven by plate spreading, the diffuse upwelling due to plate accretion, and the shearing movement generated by large-scale mantle flow. The ridge axis is free to move in the spreading direction to adjust to the maxima of tension at the lithosphere-mantle interface induced by the convective circulation. The melt distribution in the mantle and the crustal production at the ridge axis are estimated using the formalism of McKenzie and Bickle <1988>. During the experiments the record of the ridge axis positions and crustal production is used to compute synthetic maps of the isochrons and oceanic crustal thickness. Close to the ridge, the ascending convective flow consists of 80- to 100-km-long hot sheets oriented either roughly parallel or orthogonal to spreading. Most ridge segments fit with the top of hot upwelling sheets, while transient transform faults coincide with the top of cold downwelling flows. The crustal maps display lineations subparallel or slightily oblique to spreading, a few tens of million years long, and separated by ~60--50 km, resulting from the lithospheric record of the excess crust produced at the junction of hot sheets. When a junction of two hot sheets migrates outside the ridge axial plane, the crustal thickness maximum splits into two maxima along axis, and the induced lineation in the crustal map splits into two branches. The merging of lineations occurs when the ridge plane traps the junction of hot sheets. When the large-scale mantle circulation moves parallel to the ridge crest, it slowly pushs the spreading-parallel convective sheets. The resulting lineations form V shapes pointing in the same direction as the large-scale flow. When the large-scale flow parallels spreading, it slowly pushes the ridge-parallel hot sheets in the upflow direction. Thus the ridge segments attached to these hot sheets also migrate in the upflow direction. After several tens of million years the cavity flow driven by the spreading closes most of the transform segments and collects most of the ridge segments to form large continuous lines quasi-orthogonal to spreading. Using the relationships between crustal lineations and convective flow in the models, we interpret the lineations described in the satellite-derived gravity maps on the flanks of the Atlantic, Indian, and South Pacific plate boundaries analyzed in the companion paper by Briais and Rabinowicz <2002>.