Public Health Scotland data shows 81,112 people had received their first jag by April 13.
That was up 1% from 80,271 a week earlier.
It means 61% of people aged 16 and over in Falkirk have now received their first dose, using the latest Scottish population estimates.
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The figures include 20,177 people who had their second dose, meaning 15% of over-16s have now had both jags.
Across Scotland, 2.7 million people received a jag by April 13, 59% of the population.
That was an increase of 4% from 2.6 million the week before.
The data also shows that 634,000 people across Scotland have received both jags, 14% of the population.
Vaccinations are being delivered through GP practices, health centres and local clinics.
Following the first dose of the vaccine, a second jag is offered up to 12 weeks later.