Deep submicron processes have allowed FPGAs to grow in complexity and speed. However, such technology scaling has caused FPGAs to become more susceptible to the effects of process variation. In order to obtain sufficient yield values, it is now necessary to consider process variation during physical design. It is common for FPGAs to contain designs with multi-cycle paths to help increase the performance, but current SSTA techniques cannot support this type of timing constraint. We propose an extension to block-based SSTA to consider multi-cycle paths. We then use this new SSTA to optimize FPGA placement with our tool VMC-Place for designs with multi-cycle paths. Our experimental results show our multi-cycle SSTA is accurate to 0.59% for the mean and 0.0024% for the standard deviation. Our results also show that VMC-Place is able to improve the clock period by 9.42% or the performance yield by 68.51% compared to a single-cycle variation-aware placer.