Yingluck Shinawatra, who flew to New Delhi on Monday, is making her first official visit to the country to promote trade, which the Asian partners hope to double to $14 billion by 2014 from its 2010 level.
Shinawatra, who became Thailand's first female prime minister in August, was seated with Pratibha Patil, India's first woman president, as marching bands and military hardware filed past.
India was also set to put on display for the first time its Agni-IV missile which can launch a one-tonne nuclear warhead.
Agni-IV, last tested in November 2011 is part of an Indian programme to build an array of weapons including nuclear-tipped inter-continental ballistic missiles.
The national ceremony will later culminate in flypasts by US-built C-130J Super Hercules planes, Russian-supplied Sukhoi-30s and MiG-29 fighter jets.
India is spending tens of billions of dollars to modernise its military, the world's fourth largest.
Some 25,000 policemen, commandos and soldiers guarded the city against possible attacks from militant groups while its skies were a no-fly zone for the duration of the celebrations, officials said.
Last September, 12 people died and nearly 80 others were wounded when a powerful bomb went off at the fortified Delhi High Court in the heart of the Indian capital.
Combat troops were also out in strength on the streets of Indian-administered Kashmir to try to thwart anti-government protests by separatist groups who usually use the occasion to denounce rule by New Delhi.