In this article, we report on a mathematical model for the throughput and delay of LTE's Random Access Channel (RACH). The model is an improvement of a cell-level Markov model of Multichannel slotted ALOHA proposed previously in the literature. The improvements concern accounting for a possibility of contention resolution in the case when terminals select same preambles and distinguishing initially-transmitting nodes from retransmitting nodes. The improved model is verified and agrees with measurements obtained from a discrete-time event-based simulator of an LTE cell