We present a general model for an atomic memory using ultra-short pulses of light, which allows both spatial and temporal multimode storage. The process involves the storage of a faint quantum light pulse into the spin coherence of the ground state of Λ-type 3-level atoms, in the presence of a strong driving pulse. Our model gives a full description of the evolution of the field and of the atomic coherence in space and time throughout the writing and the read-out processes. It is valid for any frequency detuning, from the resonant case to the Raman case, and allows a detailed optimization of the memory efficiency.