The alert includes Pembrokeshire, Carmarthenshire and Ceredigion.
The yellow warning takes effect from 5pm this evening, Saturday July 19 until 9pm.
The forecaster said: “Heavy rain and thunderstorms may cause some localised flooding and transport disruption.”
The Met Office is also advising:
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There is a slight chance of power cuts and loss of other services to some homes and businesses
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There is a small chance that homes and businesses could be flooded, causing damage to some buildings
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Where flooding occurs, there is a slight chance of delays or cancellations to train and bus services
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Spray and flooding could lead to difficult driving conditions and some road closures
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There is a small chance that some communities will become cut off by flooded roads
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There is a small chance of fast flowing or deep floodwater causing danger to life